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mw-ui-icon-wikimedia-expand"></span> <span>Toggle Zbatime subsection</span> </button> <ul id="toc-Zbatime-sublist" class="vector-toc-list"> <li id="toc-Teoria_e_Sturm–Liuvilit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Teoria_e_Sturm–Liuvilit"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Teoria e Sturm–Liuvilit</span> </div> </a> <ul id="toc-Teoria_e_Sturm–Liuvilit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ekuacionet_diferenciale_pjesore" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ekuacionet_diferenciale_pjesore"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Ekuacionet diferenciale pjesore</span> </div> </a> <ul id="toc-Ekuacionet_diferenciale_pjesore-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Teoria_ergodike" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Teoria_ergodike"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Teoria ergodike</span> </div> </a> <ul id="toc-Teoria_ergodike-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Te_tjera" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Te_tjera"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Te tjera</span> </div> </a> <ul id="toc-Te_tjera-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Percaktime_dhe_shembuj" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Percaktime_dhe_shembuj"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Percaktime dhe shembuj</span> </div> </a> <button aria-controls="toc-Percaktime_dhe_shembuj-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Percaktime dhe shembuj subsection</span> </button> <ul id="toc-Percaktime_dhe_shembuj-sublist" class="vector-toc-list"> <li id="toc-Hapësirat_Euklidiane" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësirat_Euklidiane"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Hapësirat Euklidiane</span> </div> </a> <ul id="toc-Hapësirat_Euklidiane-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hapësira_e_vargjeve_të_pafundme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësira_e_vargjeve_të_pafundme"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Hapësira e vargjeve të pafundme</span> </div> </a> <ul id="toc-Hapësira_e_vargjeve_të_pafundme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hapësirat_e_Lebesgut" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësirat_e_Lebesgut"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Hapësirat e Lebesgut</span> </div> </a> <ul id="toc-Hapësirat_e_Lebesgut-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hapësirat_e_Sobolevit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësirat_e_Sobolevit"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Hapësirat e Sobolevit</span> </div> </a> <ul id="toc-Hapësirat_e_Sobolevit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hapësirat_e_Hardit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësirat_e_Hardit"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Hapësirat e Hardit</span> </div> </a> <ul id="toc-Hapësirat_e_Hardit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Shumat_direkte" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Shumat_direkte"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Shumat direkte</span> </div> </a> <ul id="toc-Shumat_direkte-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Produktet_tensoriale" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Produktet_tensoriale"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Produktet tensoriale</span> </div> </a> <ul id="toc-Produktet_tensoriale-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vetitë" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Vetitë"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Vetitë</span> </div> </a> <button aria-controls="toc-Vetitë-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Vetitë subsection</span> </button> <ul id="toc-Vetitë-sublist" class="vector-toc-list"> <li id="toc-Identiteti_i_Pitagorës" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiteti_i_Pitagorës"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Identiteti i Pitagorës</span> </div> </a> <ul id="toc-Identiteti_i_Pitagorës-sublist" class="vector-toc-list"> <li id="toc-Jobarazimi_i_Bezelit" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Jobarazimi_i_Bezelit"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Jobarazimi i Bezelit</span> </div> </a> <ul id="toc-Jobarazimi_i_Bezelit-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Vetia_e_kompletimit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vetia_e_kompletimit"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Vetia e kompletimit</span> </div> </a> <ul id="toc-Vetia_e_kompletimit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Identiteti_i_Paralelogramit_dhe_polarizimi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Identiteti_i_Paralelogramit_dhe_polarizimi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Identiteti i Paralelogramit dhe polarizimi</span> </div> </a> <ul id="toc-Identiteti_i_Paralelogramit_dhe_polarizimi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topologjia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topologjia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Topologjia</span> </div> </a> <ul id="toc-Topologjia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Përafrimi_më_i_mire" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Përafrimi_më_i_mire"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Përafrimi më i mire</span> </div> </a> <ul id="toc-Përafrimi_më_i_mire-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Refleksiviteti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Refleksiviteti"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Refleksiviteti</span> </div> </a> <ul id="toc-Refleksiviteti-sublist" class="vector-toc-list"> <li id="toc-Vargjet_me_konvergjencë_të_dobët" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Vargjet_me_konvergjencë_të_dobët"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6.1</span> <span>Vargjet me konvergjencë të dobët</span> </div> </a> <ul id="toc-Vargjet_me_konvergjencë_të_dobët-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Bazat_ortonormale" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Bazat_ortonormale"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bazat ortonormale</span> </div> </a> <button aria-controls="toc-Bazat_ortonormale-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Bazat ortonormale subsection</span> </button> <ul id="toc-Bazat_ortonormale-sublist" class="vector-toc-list"> <li id="toc-Dimensioni_i_Hilbertit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dimensioni_i_Hilbertit"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Dimensioni i Hilbertit</span> </div> </a> <ul id="toc-Dimensioni_i_Hilbertit-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hapësirat_e_ndashme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hapësirat_e_ndashme"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Hapësirat e ndashme</span> </div> </a> <ul id="toc-Hapësirat_e_ndashme-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Komplementi_dhe_projeksioni_ortogonal" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Komplementi_dhe_projeksioni_ortogonal"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Komplementi dhe projeksioni ortogonal</span> </div> </a> <ul id="toc-Komplementi_dhe_projeksioni_ortogonal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Operatoret_ne_hapësirat_Hilbertiane" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Operatoret_ne_hapësirat_Hilbertiane"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Operatoret ne hapësirat Hilbertiane</span> </div> </a> <button aria-controls="toc-Operatoret_ne_hapësirat_Hilbertiane-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Operatoret ne hapësirat Hilbertiane subsection</span> </button> <ul id="toc-Operatoret_ne_hapësirat_Hilbertiane-sublist" class="vector-toc-list"> <li id="toc-Operatoret_e_lidhur" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Operatoret_e_lidhur"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Operatoret e lidhur</span> </div> </a> <ul id="toc-Operatoret_e_lidhur-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Operatoret_e_palidhur" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Operatoret_e_palidhur"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Operatoret e palidhur</span> </div> </a> <ul id="toc-Operatoret_e_palidhur-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Shikoni_gjithashtu" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Shikoni_gjithashtu"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Shikoni gjithashtu</span> </div> </a> <ul id="toc-Shikoni_gjithashtu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Shënime" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Shënime"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Shënime</span> </div> </a> <ul id="toc-Shënime-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referime" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Referime"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Referime</span> </div> </a> <ul id="toc-Referime-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lidhje_të_jashtme" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lidhje_të_jashtme"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Lidhje të jashtme</span> </div> </a> <ul id="toc-Lidhje_të_jashtme-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet 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Available in 59 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-59" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">59 gjuhë</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hilbert-ruimte" title="Hilbert-ruimte – afrikanisht" lang="af" hreflang="af" data-title="Hilbert-ruimte" data-language-autonym="Afrikaans" data-language-local-name="afrikanisht" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%D8%A1_%D9%87%D9%8A%D9%84%D8%A8%D8%B1%D8%AA" title="فضاء هيلبرت – arabisht" lang="ar" hreflang="ar" data-title="فضاء هيلبرت" data-language-autonym="العربية" data-language-local-name="arabisht" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Espaciu_de_Hilbert" title="Espaciu de Hilbert – asturisht" lang="ast" hreflang="ast" data-title="Espaciu de Hilbert" data-language-autonym="Asturianu" data-language-local-name="asturisht" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Hilbert_f%C9%99zas%C4%B1" title="Hilbert fəzası – azerbajxhanisht" lang="az" hreflang="az" data-title="Hilbert fəzası" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajxhanisht" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82_%D0%B0%D1%80%D0%B0%D1%83%D1%8B%D2%93%D1%8B" title="Гильберт арауығы – bashkirisht" lang="ba" hreflang="ba" data-title="Гильберт арауығы" data-language-autonym="Башҡортса" data-language-local-name="bashkirisht" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Хилбертово пространство – bullgarisht" lang="bg" hreflang="bg" data-title="Хилбертово пространство" data-language-autonym="Български" data-language-local-name="bullgarisht" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%BF%E0%A6%B2%E0%A6%AC%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%9F_%E0%A6%9C%E0%A6%97%E0%A7%8E" title="হিলবার্ট জগৎ – bengalisht" lang="bn" hreflang="bn" data-title="হিলবার্ট জগৎ" data-language-autonym="বাংলা" data-language-local-name="bengalisht" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Espai_de_Hilbert" title="Espai de Hilbert – katalonisht" lang="ca" hreflang="ca" data-title="Espai de Hilbert" data-language-autonym="Català" data-language-local-name="katalonisht" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%86%D8%B4%D8%A7%DB%8C%DB%8C%DB%8C_%DA%BE%DB%8C%D9%84%D8%A8%DB%8E%D8%B1%D8%AA" title="بۆشاییی ھیلبێرت – kurdishte qendrore" lang="ckb" hreflang="ckb" data-title="بۆشاییی ھیلبێرت" data-language-autonym="کوردی" data-language-local-name="kurdishte qendrore" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hilbert%C5%AFv_prostor" title="Hilbertův prostor – çekisht" lang="cs" hreflang="cs" data-title="Hilbertův prostor" data-language-autonym="Čeština" data-language-local-name="çekisht" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hilbertrum" title="Hilbertrum – danisht" lang="da" hreflang="da" data-title="Hilbertrum" data-language-autonym="Dansk" data-language-local-name="danisht" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hilbertraum" title="Hilbertraum – gjermanisht" lang="de" hreflang="de" data-title="Hilbertraum" data-language-autonym="Deutsch" data-language-local-name="gjermanisht" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CF%8E%CF%81%CE%BF%CF%82_%CE%A7%CE%AF%CE%BB%CE%BC%CF%80%CE%B5%CF%81%CF%84" title="Χώρος Χίλμπερτ – greqisht" lang="el" hreflang="el" data-title="Χώρος Χίλμπερτ" data-language-autonym="Ελληνικά" data-language-local-name="greqisht" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="artikuj të mirë"><a href="https://en.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – anglisht" lang="en" hreflang="en" data-title="Hilbert space" data-language-autonym="English" data-language-local-name="anglisht" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hilberta_spaco" title="Hilberta spaco – esperanto" lang="eo" hreflang="eo" data-title="Hilberta spaco" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Espacio_de_Hilbert" title="Espacio de Hilbert – spanjisht" lang="es" hreflang="es" data-title="Espacio de Hilbert" data-language-autonym="Español" data-language-local-name="spanjisht" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hilberti_ruum" title="Hilberti ruum – estonisht" lang="et" hreflang="et" data-title="Hilberti ruum" data-language-autonym="Eesti" data-language-local-name="estonisht" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hilberten_espazio" title="Hilberten espazio – baskisht" lang="eu" hreflang="eu" data-title="Hilberten espazio" data-language-autonym="Euskara" data-language-local-name="baskisht" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%DB%8C_%D9%87%DB%8C%D9%84%D8%A8%D8%B1%D8%AA" title="فضای هیلبرت – persisht" lang="fa" hreflang="fa" data-title="فضای هیلبرت" data-language-autonym="فارسی" data-language-local-name="persisht" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hilbertin_avaruus" title="Hilbertin avaruus – finlandisht" lang="fi" hreflang="fi" data-title="Hilbertin avaruus" data-language-autonym="Suomi" data-language-local-name="finlandisht" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Espace_de_Hilbert" title="Espace de Hilbert – frëngjisht" lang="fr" hreflang="fr" data-title="Espace de Hilbert" data-language-autonym="Français" data-language-local-name="frëngjisht" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Espazo_de_Hilbert" title="Espazo de Hilbert – galicisht" lang="gl" hreflang="gl" data-title="Espazo de Hilbert" data-language-autonym="Galego" data-language-local-name="galicisht" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט – hebraisht" lang="he" hreflang="he" data-title="מרחב הילברט" data-language-autonym="עברית" data-language-local-name="hebraisht" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hilbert-t%C3%A9r" title="Hilbert-tér – hungarisht" lang="hu" hreflang="hu" data-title="Hilbert-tér" data-language-autonym="Magyar" data-language-local-name="hungarisht" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%AB%D5%AC%D5%A2%D5%A5%D6%80%D5%BF%D5%B5%D5%A1%D5%B6_%D5%BF%D5%A1%D6%80%D5%A1%D5%AE%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Հիլբերտյան տարածություն – armenisht" lang="hy" hreflang="hy" data-title="Հիլբերտյան տարածություն" data-language-autonym="Հայերեն" data-language-local-name="armenisht" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ruang_Hilbert" title="Ruang Hilbert – indonezisht" lang="id" hreflang="id" data-title="Ruang Hilbert" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezisht" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hilbert-r%C3%BAm" title="Hilbert-rúm – islandisht" lang="is" hreflang="is" data-title="Hilbert-rúm" data-language-autonym="Íslenska" data-language-local-name="islandisht" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spazio_di_Hilbert" title="Spazio di Hilbert – italisht" lang="it" hreflang="it" data-title="Spazio di Hilbert" data-language-autonym="Italiano" data-language-local-name="italisht" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%92%E3%83%AB%E3%83%99%E3%83%AB%E3%83%88%E7%A9%BA%E9%96%93" title="ヒルベルト空間 – japonisht" lang="ja" hreflang="ja" data-title="ヒルベルト空間" data-language-autonym="日本語" data-language-local-name="japonisht" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%9E%90%EB%B2%A0%EB%A5%B4%ED%8A%B8_%EA%B3%B5%EA%B0%84" title="힐베르트 공간 – koreanisht" lang="ko" hreflang="ko" data-title="힐베르트 공간" data-language-autonym="한국어" data-language-local-name="koreanisht" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82_%D0%BC%D0%B5%D0%B9%D0%BA%D0%B8%D0%BD%D0%B4%D0%B8%D0%B3%D0%B8" title="Гильберт мейкиндиги – kirgizisht" lang="ky" hreflang="ky" data-title="Гильберт мейкиндиги" data-language-autonym="Кыргызча" data-language-local-name="kirgizisht" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hilberto_erdv%C4%97" title="Hilberto erdvė – lituanisht" lang="lt" hreflang="lt" data-title="Hilberto erdvė" data-language-autonym="Lietuvių" data-language-local-name="lituanisht" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%B8%D0%B9%D0%BD_%D0%BE%D1%80%D0%BE%D0%BD_%D0%B7%D0%B0%D0%B9" title="Хилбертийн орон зай – mongolisht" lang="mn" hreflang="mn" data-title="Хилбертийн орон зай" data-language-autonym="Монгол" data-language-local-name="mongolisht" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ruang_Hilbert" title="Ruang Hilbert – malajisht" lang="ms" hreflang="ms" data-title="Ruang Hilbert" data-language-autonym="Bahasa Melayu" data-language-local-name="malajisht" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hilbertruimte" title="Hilbertruimte – holandisht" lang="nl" hreflang="nl" data-title="Hilbertruimte" data-language-autonym="Nederlands" data-language-local-name="holandisht" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hilbertrom" title="Hilbertrom – norvegjishte nynorsk" lang="nn" hreflang="nn" data-title="Hilbertrom" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegjishte nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hilbert-rom" title="Hilbert-rom – norvegjishte letrare" lang="nb" hreflang="nb" data-title="Hilbert-rom" data-language-autonym="Norsk bokmål" data-language-local-name="norvegjishte letrare" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B9%E0%A8%BF%E0%A8%B2%E0%A8%AC%E0%A8%B0%E0%A8%9F_%E0%A8%B8%E0%A8%AA%E0%A9%87%E0%A8%B8" title="ਹਿਲਬਰਟ ਸਪੇਸ – punxhabisht" lang="pa" hreflang="pa" data-title="ਹਿਲਬਰਟ ਸਪੇਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punxhabisht" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przestrze%C5%84_Hilberta" title="Przestrzeń Hilberta – polonisht" lang="pl" hreflang="pl" data-title="Przestrzeń Hilberta" data-language-autonym="Polski" data-language-local-name="polonisht" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DB%81%D9%84%D8%A8%D8%B1%D9%B9_%D8%B3%D9%BE%DB%8C%D8%B3" title="ہلبرٹ سپیس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ہلبرٹ سپیس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Espa%C3%A7o_de_Hilbert" title="Espaço de Hilbert – portugalisht" lang="pt" hreflang="pt" data-title="Espaço de Hilbert" data-language-autonym="Português" data-language-local-name="portugalisht" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Spa%C8%9Biu_Hilbert" title="Spațiu Hilbert – rumanisht" lang="ro" hreflang="ro" data-title="Spațiu Hilbert" data-language-autonym="Română" data-language-local-name="rumanisht" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Гильбертово пространство – rusisht" lang="ru" hreflang="ru" data-title="Гильбертово пространство" data-language-autonym="Русский" data-language-local-name="rusisht" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – skotisht" lang="sco" hreflang="sco" data-title="Hilbert space" data-language-autonym="Scots" data-language-local-name="skotisht" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hilbertov_prostor" title="Hilbertov prostor – serbo-kroatisht" lang="sh" hreflang="sh" data-title="Hilbertov prostor" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-kroatisht" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hilbert space" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hilbertov_priestor" title="Hilbertov priestor – sllovakisht" lang="sk" hreflang="sk" data-title="Hilbertov priestor" data-language-autonym="Slovenčina" data-language-local-name="sllovakisht" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hilbertov_prostor" title="Hilbertov prostor – sllovenisht" lang="sl" hreflang="sl" data-title="Hilbertov prostor" data-language-autonym="Slovenščina" data-language-local-name="sllovenisht" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Хилбертов простор – serbisht" lang="sr" hreflang="sr" data-title="Хилбертов простор" data-language-autonym="Српски / srpski" data-language-local-name="serbisht" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hilbertrum" title="Hilbertrum – suedisht" lang="sv" hreflang="sv" data-title="Hilbertrum" data-language-autonym="Svenska" data-language-local-name="suedisht" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espasyong_Hilbert" title="Espasyong Hilbert – Tagalog" lang="tl" hreflang="tl" data-title="Espasyong Hilbert" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hilbert_uzay%C4%B1" title="Hilbert uzayı – turqisht" lang="tr" hreflang="tr" data-title="Hilbert uzayı" data-language-autonym="Türkçe" data-language-local-name="turqisht" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%96%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D1%96%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80" title="Гільбертів простір – ukrainisht" lang="uk" hreflang="uk" data-title="Гільбертів простір" data-language-autonym="Українська" data-language-local-name="ukrainisht" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Gilbert_fazosi" title="Gilbert fazosi – uzbekisht" lang="uz" hreflang="uz" data-title="Gilbert fazosi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekisht" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%C3%B4ng_gian_Hilbert" title="Không gian Hilbert – vietnamisht" lang="vi" hreflang="vi" data-title="Không gian Hilbert" data-language-autonym="Tiếng Việt" 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Nga Wikipedia, enciklopedia e lirë</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sq" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Skeda:Harmonic_partials_on_strings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/220px-Harmonic_partials_on_strings.svg.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/330px-Harmonic_partials_on_strings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/440px-Harmonic_partials_on_strings.svg.png 2x" data-file-width="620" data-file-height="590" /></a><figcaption>Hapësira e Hilbertit mund të përdoret për të studiuar lëvizjen harmonike të kordës vibruese.</figcaption></figure> <p>Në <a href="/wiki/Matematika" title="Matematika">matematikë</a> koncepti i <b>hapësirës së Hilbertit</b>, përgjithëson nocionin e <a href="/wiki/Hap%C3%ABsira_Euklidiane" title="Hapësira Euklidiane">hapësirës Euklidiane</a>. Ky nocion zgjeron metodat e algjebrës vektoriale nga plani dy dimensional dhe hapësira tredimensionale në hapësirat me numër të pafundëm të dimensioneve. </p><p>Në mënyrë më formale, hapësira e Hilbertit është një <a href="/w/index.php?title=Hap%C3%ABsir%C3%AB_e_produktit_t%C3%AB_brendsh%C3%ABm&action=edit&redlink=1" class="new" title="Hapësirë e produktit të brendshëm (nuk është shkruar akoma)">hapësirë e produktit të brendshëm</a> në një <a href="/w/index.php?title=Hap%C3%ABsir%C3%AB_vektoriale&action=edit&redlink=1" class="new" title="Hapësirë vektoriale (nuk është shkruar akoma)">hapësirë vektoriale</a> abstrakte në të cilën distancat dhe këndet mund të maten. Pra kjo është një "<a href="/w/index.php?title=Hap%C3%ABsira_metrike_e_plot%C3%AB&action=edit&redlink=1" class="new" title="Hapësira metrike e plotë (nuk është shkruar akoma)">hapësirë komplete</a>", që nënkupton se nëqoftëse një varg vektorësh është i tipit <a href="/w/index.php?title=Vargjet_Koshi&action=edit&redlink=1" class="new" title="Vargjet Koshi (nuk është shkruar akoma)">Koshi</a>, atëherë ai konvergjon d.m.th. ka <a href="/w/index.php?title=Limiti_i_vargut&action=edit&redlink=1" class="new" title="Limiti i vargut (nuk është shkruar akoma)">limit</a> brenda asaj hapësire. </p><p>Hapësirat e Hilbertit shfaqen shpesh në mënyrë te natyrshme në <a href="/wiki/Matematika" title="Matematika">matematikë</a>, <a href="/wiki/Fizika" title="Fizika">fizikë</a>, dhe në <a href="/wiki/Inxhinieria" title="Inxhinieria">inxhinieri</a>. Zakonisht kjo është si <a href="/w/index.php?title=Hap%C3%ABsira_funksionale&action=edit&redlink=1" class="new" title="Hapësira funksionale (nuk është shkruar akoma)">hapësira funksionale</a> me dimensione të pafundme. Këto cilësohen si mjete të pazëvendësueshme në teorinë e <a href="/w/index.php?title=Ekuacioneve_diferenciale_pjesore&action=edit&redlink=1" class="new" title="Ekuacioneve diferenciale pjesore (nuk është shkruar akoma)">ekuacioneve diferenciale pjesore</a>, <a href="/w/index.php?title=Formulimi_matematik_i_mekanikes_kuantike&action=edit&redlink=1" class="new" title="Formulimi matematik i mekanikes kuantike (nuk është shkruar akoma)">mekanikes kuantike</a>, dhe <a href="/w/index.php?title=Pro%C3%A7esimit_t%C3%AB_sinjaleve&action=edit&redlink=1" class="new" title="Proçesimit të sinjaleve (nuk është shkruar akoma)">proçesimit të sinjaleve</a>. Njohja e një strukture të përbashkët algjebrike midis këtyre fushave të ndryshme dha një kuptim me të gjerë të konceptuar. Suksesi i metodave të hapësirës së Hilbertit çoi ne periudhën e arte të <a href="/wiki/Analiza_funksionale" title="Analiza funksionale">analizës funksionale</a>. </p><p>Intuita gjeometrike luan një rol shumë te rëndësishëm në shumë aspekte të teorisë se hapësirave të Hilbertit. Një element i hapësirës së Hilbertit mund të veçohet në mënyrë unike nga koordinatat në lidhje me një <a href="/w/index.php?title=Baze_ortonormale&action=edit&redlink=1" class="new" title="Baze ortonormale (nuk është shkruar akoma)">vektor bazë</a>, në ngjashshmëri me koordinatat karteziane në një plan. Kur kjo bazë është e numërueshme, kjo do të thotë se hapësira e Hilbertit mund të shprehet me terma të <a href="/w/index.php?title=Vargjet_e_pafundme&action=edit&redlink=1" class="new" title="Vargjet e pafundme (nuk është shkruar akoma)">vargjeve të pafundme</a> e që janë <a href="/w/index.php?title=Hap%C3%ABsira_Lp&action=edit&redlink=1" class="new" title="Hapësira Lp (nuk është shkruar akoma)">hapësira të Lebegut</a>. <a href="/w/index.php?title=Operator%C3%ABt_linear%C3%AB&action=edit&redlink=1" class="new" title="Operatorët linearë (nuk është shkruar akoma)">Operatorët linearë</a> në një hapësirë të Hilbertit janë gjithashtu objekte konkrete. Në raste të favorshme, ato janë thjesht transformime që zgjerojnë hapësirën me faktorë të ndryshëm. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hyrje_dhe_historia">Hyrje dhe historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=1" title="Redakto pjesën: Hyrje dhe historia" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=1" title="Edit section's source code: Hyrje dhe historia"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Skeda:Hilbert.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/220px-Hilbert.jpg" decoding="async" width="220" height="298" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/330px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/7/79/Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption><a href="/wiki/David_Hilberti" class="mw-redirect" title="David Hilberti">David Hilberti</a>, matematikani puna themelore e të cilit në studimin e <a href="/w/index.php?title=Ekuacioneve_integrale&action=edit&redlink=1" class="new" title="Ekuacioneve integrale (nuk është shkruar akoma)">ekuacioneve integrale</a> dhe <a href="/w/index.php?title=Formave_kuadratike&action=edit&redlink=1" class="new" title="Formave kuadratike (nuk është shkruar akoma)">formave kuadratike</a> çoi tek koncepti i hapësirave të Hilbertit.</figcaption></figure> <p><a href="/wiki/Hap%C3%ABsira_Euklidiane" title="Hapësira Euklidiane">Hapësira Euklidiane</a> e zakonshme shërben si një model për nocionin e hapësirës se Hilbertit. Në hapësirën Euklidiane, të dhëne në <b>R</b><sup>3</sup>, <a href="/wiki/Distanca" title="Distanca">distanca</a> në mes pikave dhe <a href="/wiki/K%C3%ABndi" title="Këndi">këndi</a> në mes vektorëve mund të shprehen nëpërmjet <a href="/w/index.php?title=Produktit_t%C3%AB_brendsh%C3%ABm&action=edit&redlink=1" class="new" title="Produktit të brendshëm (nuk është shkruar akoma)">produktit të brendshëm</a>, një <a href="/w/index.php?title=Pasqyrim_bilinear&action=edit&redlink=1" class="new" title="Pasqyrim bilinear (nuk është shkruar akoma)">veprim</a> mbi një çift vektorësh vlerat e të cilëve janë <a href="/w/index.php?title=Numra_reale&action=edit&redlink=1" class="new" title="Numra reale (nuk është shkruar akoma)">numra reale</a>. Probleme nga <a href="/wiki/Gjeometria_analitike" title="Gjeometria analitike">gjeometria analitike</a>, si përcaktimi nëqoftesë dy drejtëza janë <a href="/w/index.php?title=Ortogonaliteti&action=edit&redlink=1" class="new" title="Ortogonaliteti (nuk është shkruar akoma)">pingule</a> ose gjetja e një pike në një plan të dhëne e cila është me afër origjinës, mund te shprehen dhe të zgjidhen duke përdorur prodhimin e brendshëm vektorial.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Një tipar tjetër i rëndësishëm i <b>R</b><sup>3</sup> është që ajo posedon strukturë të mjaftueshme për të ruajtur metodat e <a href="/w/index.php?title=Analiz%C3%ABs&action=edit&redlink=1" class="new" title="Analizës (nuk është shkruar akoma)">analizës</a>, për shkak të ekzistencës së <a href="/w/index.php?title=Limiti_(matematika)&action=edit&redlink=1" class="new" title="Limiti (matematika) (nuk është shkruar akoma)">limiteve</a>. Hapësirat e Hilbertit janë përgjithshme te <b>R</b><sup>3</sup> të cilat përmbajnë një operator analog me prodhimin vektorial në hapësirën Euklidiane (kjo zakonisht quhet prodhimi i brendshëm) te cilat janë “komplete" në sensin që limitet që duhen për zbatimin e analizës ekzistojnë. </p><p>Para zhvillimit të hapësirave të Hilbertit, përgjithësime të tjera të <b>R</b><sup>3</sup> ishin te njohura nga matematikanët dhe fizikanet. Në veçanti, ideja e <a href="/w/index.php?title=Hap%C3%ABsira_lineare&action=edit&redlink=1" class="new" title="Hapësira lineare (nuk është shkruar akoma)">hapësirave abstrakte lineare</a> kishte marrë hov nga fundi i shekullit XIX :<sup class="noprint Inline-Template noprint Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citim_i_duhur" title="Wikipedia:Citim i duhur"><span title="Me këtë kërjohen referenca nga burime të besueshme">nevojitet citimi</span></a></i>]</sup> kjo është një hapësire elementet e së cilës mund të mblidhen dhe të shumëzohen me skalare (si <a href="/w/index.php?title=Numri_real&action=edit&redlink=1" class="new" title="Numri real (nuk është shkruar akoma)">numrat real</a> ose <a href="/wiki/Numri_kompleks" class="mw-redirect" title="Numri kompleks">komplekse</a>) pa i identifikuar këto elemente me <a href="/wiki/Vektori_(gjeometri)" class="mw-redirect" title="Vektori (gjeometri)">vektorë "gjeometrike"</a>, si vektorët e pozicionit dhe momentit në sisteme fizike. Objekte të tjera të studiuara nga matematikanët në fillim të shekullit XX, në veçanti hapësirat e <a href="/w/index.php?title=Vargu(matematike)&action=edit&redlink=1" class="new" title="Vargu(matematike) (nuk është shkruar akoma)">vargjeve</a> (duke përfshire <a href="/w/index.php?title=Seria_(matematike)&action=edit&redlink=1" class="new" title="Seria (matematike) (nuk është shkruar akoma)">seritë</a>) dhe hapësirat e funksioneve,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> të cilat mund të kuptohen si hapësira lineare. Funksionet, për shembull, mund të mblidhen ose të shumëzohen me skalarë, veprime këto që i binden ligjeve algjebrike të mbledhjes dhe shumëzimit të vektorëve hapësinorë. </p><p>Në dekadën e parë të shekullit XX, zhvillime paralele sollën deri të paraqitja e hapësirave të Hilbertit. E parë nga ky vëzhgim, gjate studimit të <a href="/w/index.php?title=Ekuacioneve_integrale&action=edit&redlink=1" class="new" title="Ekuacioneve integrale (nuk është shkruar akoma)">ekuacioneve integrale</a> nga <a href="/wiki/David_Hilberti" class="mw-redirect" title="David Hilberti">David Hilberti</a> dhe <a href="/w/index.php?title=Erhard_Schmidt&action=edit&redlink=1" class="new" title="Erhard Schmidt (nuk është shkruar akoma)">Erhard Schmidt</a>,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> se dy funksione reale të vazhdueshme <i>f</i> dhe <i>g</i> në një interval [<i>a</i>,<i>b</i>] që janë të integrueshëm kanë një <i>produkt të brendshëm</i> : </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle f,g\rangle =\int _{a}^{b}f(x)g(x)\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>f</mi> <mo>,</mo> <mi>g</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle f,g\rangle =\int _{a}^{b}f(x)g(x)\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb5664507c246433823ea44c7492e2094bc769dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.73ex; height:6.343ex;" alt="{\displaystyle \langle f,g\rangle =\int _{a}^{b}f(x)g(x)\,dx}"></span></dd></dl> <p>i cili ka shumë nga vetitë familjare të prodhimit vektorial Euklidian. Në veçanti ideja e familjeve të funksioneve <a href="/w/index.php?title=Ortogonaliteti&action=edit&redlink=1" class="new" title="Ortogonaliteti (nuk është shkruar akoma)">ortogonale</a> ka një kuptim të caktuar. Shmidt përdori ngjashmërinë midis produktit të brendshëm me produktin vektorial Euklidian për të provuar analogun e <a href="/w/index.php?title=Dekompozimit_spektral&action=edit&redlink=1" class="new" title="Dekompozimit spektral (nuk është shkruar akoma)">dekompozimit spektral</a> për një operator të formës </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)\mapsto \int _{a}^{b}K(x,y)f(y)\,dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">↦</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>K</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)\mapsto \int _{a}^{b}K(x,y)f(y)\,dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/623eb5c416d4a989222bcd10ae8f02fbfc92dd0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.217ex; height:6.343ex;" alt="{\displaystyle f(x)\mapsto \int _{a}^{b}K(x,y)f(y)\,dy}"></span></dd></dl> <p>ku <i>K</i> është një funksion i vazhdueshëm simetrik në lidhje me <i>x</i> dhe <i>y</i>. <a href="/w/index.php?title=Zgjerimi_ajgenfunksonal&action=edit&redlink=1" class="new" title="Zgjerimi ajgenfunksonal (nuk është shkruar akoma)">Zgjerimi ajgenfunksonal</a> që rrjedh nga kjo e shpreh funksionin <i>K</i> si një seri të formës </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K(x,y)=\sum _{n}\lambda _{n}\varphi _{n}(x)\varphi _{n}(y)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munder> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K(x,y)=\sum _{n}\lambda _{n}\varphi _{n}(x)\varphi _{n}(y)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2fefe5a3f9269b7d083796b8c20ed7833ff3bfa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:28.777ex; height:5.509ex;" alt="{\displaystyle K(x,y)=\sum _{n}\lambda _{n}\varphi _{n}(x)\varphi _{n}(y)\,}"></span></dd></dl> <p>ku funksionet <i>φ</i><sub><i>n</i></sub> janë pingule në sensing që <span class="nowrap">〈<i>φ</i><sub><i>n</i></sub>,<i>φ</i><sub><i>m</i></sub>〉 = 0</span> for all <span class="nowrap"><i>n</i> ≠ <i>m</i></span>. Megjithatë, ekzistojnë zgjerime ajgenfunksionale të cilat nuk konvergjojnë në kuptimin e zakonshëm te një funksion që është i integrueshëm në katror : Ajo që mungon këtu është vetia e kompletimit e cila siguron konvergjencën.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Zhvillimi i dyte që <a href="/w/index.php?title=Integrali_i_Lebesgut&action=edit&redlink=1" class="new" title="Integrali i Lebesgut (nuk është shkruar akoma)">integrali i Lebesgut</a>, një alternative e <a href="/w/index.php?title=Integrali_i_Rimanit&action=edit&redlink=1" class="new" title="Integrali i Rimanit (nuk është shkruar akoma)">integralit të Rimanit</a> e paraqitur nga <a href="/wiki/Henri_Lebesgue" title="Henri Lebesgue">Henri Lebesgue</a> në 1904.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Integrali i Lebesgut beri të mundur integrimin e funksioneve që nuk janë të vazhdueshme. Ne 1907, <a href="/w/index.php?title=Frigyes_Riesz&action=edit&redlink=1" class="new" title="Frigyes Riesz (nuk është shkruar akoma)">Frigyes Riesz</a> dhe <a href="/w/index.php?title=Ernst_Sigismund_Fischer&action=edit&redlink=1" class="new" title="Ernst Sigismund Fischer (nuk është shkruar akoma)">Ernst Sigismund Fischer</a> provuan në mënyre të pavarur se hapësira L<sup>2</sup> e funksionit të integrueshëm në katror Lebesgian është një <a href="/w/index.php?title=Hap%C3%ABsire_metrike_komplete&action=edit&redlink=1" class="new" title="Hapësire metrike komplete (nuk është shkruar akoma)">hapësire metrike komplete</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Rrjedhoje e kësaj që bashkëkoordinimi midis gjeometrisë dhe vetisë së kompletimit, rezultati i shekullit të 19te i <a href="/wiki/Jozef_Fourier" class="mw-redirect" title="Jozef Fourier">Jozef Fourier</a>, <a href="/w/index.php?title=Friedrich_Bessel&action=edit&redlink=1" class="new" title="Friedrich Bessel (nuk është shkruar akoma)">Friedrich Bessel</a> dhe <a href="/w/index.php?title=Marc-Antoine_Parseval&action=edit&redlink=1" class="new" title="Marc-Antoine Parseval (nuk është shkruar akoma)">Marc-Antoine Parseval</a> mbi <a href="/w/index.php?title=Serit%C3%AB_trigonometrike&action=edit&redlink=1" class="new" title="Seritë trigonometrike (nuk është shkruar akoma)">seritë trigonometrike</a> mund të pershatet qartë në hapësira me të përgjithshme, që rezultojnë në një aparat gjeometriko-analitik të njohur si <a href="/w/index.php?title=Teorema_Riesz-Fischer&action=edit&redlink=1" class="new" title="Teorema Riesz-Fischer (nuk është shkruar akoma)">teorema Riesz-Fischer </a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Rezultate te tjera themelore u provuan ne fillim te shekullit XX. Për shembull, <a href="/w/index.php?title=Teorema_e_reprezentimit_e_Riesz&action=edit&redlink=1" class="new" title="Teorema e reprezentimit e Riesz (nuk është shkruar akoma)">teorema e reprezentimit e Riesz</a> u arrit në mënyre të pavarur nga <a href="/w/index.php?title=Maurice_Fr%C3%A9chet&action=edit&redlink=1" class="new" title="Maurice Fréchet (nuk është shkruar akoma)">Maurice Fréchet</a> dhe <a href="/w/index.php?title=Frigyes_Riesz&action=edit&redlink=1" class="new" title="Frigyes Riesz (nuk është shkruar akoma)">Frigyes Riesz</a> në 1907.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> vuri termin <i>hapësira abstrakte e Hilbertit</i> në veprën e tij të famshme mbi <a href="/w/index.php?title=Operatori_i_vete-adjointuar&action=edit&redlink=1" class="new" title="Operatori i vete-adjointuar (nuk është shkruar akoma)">operatoret Hermitian</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Von Neumann që një nga matematikanët e vetëm në ato kohe që vuri në dukje rëndësinë e rezultatit si rrjedhoje e punës së tij thelbësore në themelimet e e mekanikës kuantike,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> gjate punës së tij me <a href="/w/index.php?title=Eugene_Wigner&action=edit&redlink=1" class="new" title="Eugene Wigner (nuk është shkruar akoma)">Eugene Wigner</a>. Emri "Hilbert space" u adaptua nga të tjerët, për shembull nga Hermann Weyl në librin e tij mbi mekanikën kuantike dhe teorinë e grupeve.<sup id="cite_ref-Weyl31_11-0" class="reference"><a href="#cite_note-Weyl31-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Rëndësia e konceptit të hapësirave të Hilbertit u nënvizua nga realizmi që ajo ofron një nga <a href="/w/index.php?title=Formulimi_matematik_i_mekanik%C3%ABs_kuantike&action=edit&redlink=1" class="new" title="Formulimi matematik i mekanikës kuantike (nuk është shkruar akoma)">formulimet më të mira të mekanikës kuantike</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> shkurt, gjendjet e një sistemi janë vektorë në një hapësire të caktuar Hilbertiane, të observueshmet janë <a href="/w/index.php?title=Operatore_hermitiane&action=edit&redlink=1" class="new" title="Operatore hermitiane (nuk është shkruar akoma)">operatore hermitiane</a> në atë hapësire, <a href="/wiki/Simetria" title="Simetria">simetritë</a> e sistemit janë <a href="/w/index.php?title=Operatore_unitare&action=edit&redlink=1" class="new" title="Operatore unitare (nuk është shkruar akoma)">operatore unitare</a>, dhe <a href="/w/index.php?title=Matjet_kuantike&action=edit&redlink=1" class="new" title="Matjet kuantike (nuk është shkruar akoma)">matjet</a> janë <a href="/w/index.php?title=Projeksione_ortogonale&action=edit&redlink=1" class="new" title="Projeksione ortogonale (nuk është shkruar akoma)">projeksione ortogonale</a>. Lidhja midis simetrive mekaniko-kuantike dhe operatoreve unitare dhanë një impetus direkt për zhvillimin e <a href="/w/index.php?title=Teoris%C3%AB_s%C3%AB_reprezentimit&action=edit&redlink=1" class="new" title="Teorisë së reprezentimit (nuk është shkruar akoma)">teorisë së reprezentimit</a> <a href="/w/index.php?title=Reprezentimit_unitar&action=edit&redlink=1" class="new" title="Reprezentimit unitar (nuk është shkruar akoma)">unitar</a> të <a href="/w/index.php?title=Teoria_e_grupeve_(matematik%C3%AB)&action=edit&redlink=1" class="new" title="Teoria e grupeve (matematikë) (nuk është shkruar akoma)">grupeve</a>, të filluar më 1928 me punën e Hermann Weyl.<sup id="cite_ref-Weyl31_11-1" class="reference"><a href="#cite_note-Weyl31-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Nga ana tjetër, në fillim të viteve 1930 u be e çart se disa veti klasike të <a href="/w/index.php?title=Sistemeve_dinamike&action=edit&redlink=1" class="new" title="Sistemeve dinamike (nuk është shkruar akoma)">sistemeve dinamike</a> mund të analizohen duke përdorur teknika të hapësirës së Hilbertit në kontekstin e <a href="/w/index.php?title=Teoris%C3%AB_ergodike&action=edit&redlink=1" class="new" title="Teorisë ergodike (nuk është shkruar akoma)">teorisë ergodike</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Zbatime">Zbatime</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=2" title="Redakto pjesën: Zbatime" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=2" title="Edit section's source code: Zbatime"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Skeda:HAtomOrbitals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/HAtomOrbitals.png/220px-HAtomOrbitals.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/cf/HAtomOrbitals.png 1.5x" data-file-width="316" data-file-height="316" /></a><figcaption> <a href="/w/index.php?title=Orbitalet_atomike&action=edit&redlink=1" class="new" title="Orbitalet atomike (nuk është shkruar akoma)">Orbitalet</a> e një <a href="/wiki/Elektroni" title="Elektroni">elektroni</a> në një <a href="/w/index.php?title=Atom_hidrogjeni&action=edit&redlink=1" class="new" title="Atom hidrogjeni (nuk është shkruar akoma)">atom hidrogjeni</a> janë <a href="/w/index.php?title=Ajgenfunksione&action=edit&redlink=1" class="new" title="Ajgenfunksione (nuk është shkruar akoma)">ajgenfunksione</a> të <a href="/w/index.php?title=Energjia_(fizik%C3%AB)&action=edit&redlink=1" class="new" title="Energjia (fizikë) (nuk është shkruar akoma)">energjisë</a>. Energjia jepet nga <a href="/wiki/Ekuacioni_i_Shrodingerit" title="Ekuacioni i Shrodingerit">operatori i Shrodingerit</a> (me pavarësi ohore) i cili vepron në një nënhapësire të dendur te hapësirës Hilbertaine të funksioneve të integrueshëm-katror në <b>R</b><sup>3</sup>, ku spektri i saj përcakton nivelet e mundshme të energjisë.</figcaption></figure> <p>Shumë nga aplikimet e hapësirës se Hilbertit shfrytëzojnë faktin se hapësirat e Hilbertit suportojnë përgjithësime të koncepteve të thjeshta gjeometrike si <a href="/w/index.php?title=Operatori_projektues&action=edit&redlink=1" class="new" title="Operatori projektues (nuk është shkruar akoma)">projektimin</a> dhe <a href="/w/index.php?title=Ndryshimi_i_baz%C3%ABs&action=edit&redlink=1" class="new" title="Ndryshimi i bazës (nuk është shkruar akoma)">ndryshimi i bazës</a> në krahasim me analoget e fundem dimensionale. Në veçanti, <a href="/w/index.php?title=Teoria_spektrale&action=edit&redlink=1" class="new" title="Teoria spektrale (nuk është shkruar akoma)">teoria spektrale</a> e <a href="/w/index.php?title=Operatorit_linear&action=edit&redlink=1" class="new" title="Operatorit linear (nuk është shkruar akoma)">operatorit linear</a> të <a href="/w/index.php?title=Funksioni_i_vazhduesh%C3%ABm&action=edit&redlink=1" class="new" title="Funksioni i vazhdueshëm (nuk është shkruar akoma)">funksioni i vazhdueshëm</a> <a href="/w/index.php?title=Operatori_vete-adjoint&action=edit&redlink=1" class="new" title="Operatori vete-adjoint (nuk është shkruar akoma)">vete-adjointuar (?)</a> në një hapësire Hilberti përgjithëson dekompozimin spektral të zakonshëm tek një <a href="/w/index.php?title=Matrica_(matematik%C3%AB)&action=edit&redlink=1" class="new" title="Matrica (matematikë) (nuk është shkruar akoma)">matricë</a>, gjë kjo e cila luan një rol madhor në aplikimet e teorisë në fusha tjera të matematikës dhe fizikës. </p> <div class="mw-heading mw-heading3"><h3 id="Teoria_e_Sturm–Liuvilit"><span id="Teoria_e_Sturm.E2.80.93Liuvilit"></span>Teoria e Sturm–Liuvilit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=3" title="Redakto pjesën: Teoria e Sturm–Liuvilit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=3" title="Edit section's source code: Teoria e Sturm–Liuvilit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="dablink"> <dl><dd><i>Artikuj</i> <i>kryesor</i>e: <i><a href="/w/index.php?title=Teoria_e_Sturm%E2%80%93Liouville&action=edit&redlink=1" class="new" title="Teoria e Sturm–Liouville (nuk është shkruar akoma)">Teoria e Sturm–Liouville</a></i></dd></dl></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Skeda:Harmonic_partials_on_strings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/220px-Harmonic_partials_on_strings.svg.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/330px-Harmonic_partials_on_strings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/440px-Harmonic_partials_on_strings.svg.png 2x" data-file-width="620" data-file-height="590" /></a><figcaption> <a href="/w/index.php?title=Overtoni&action=edit&redlink=1" class="new" title="Overtoni (nuk është shkruar akoma)">Overtoni</a> i një korde vibruese. Këto janë <a href="/w/index.php?title=Ajgenfunksione&action=edit&redlink=1" class="new" title="Ajgenfunksione (nuk është shkruar akoma)">ajgenfunksione</a> të problemit Sturm–Ljuville. Ajgenvlerat 1, 1/2, 1/3... formojnë <a href="/w/index.php?title=Serite_harmonike_(muzike)&action=edit&redlink=1" class="new" title="Serite harmonike (muzike) (nuk është shkruar akoma)">serite harmonike</a> (muzikore).</figcaption></figure> <p>Në teorinë e <a href="/w/index.php?title=Ekuacioneve_diferenciale_t%C3%AB_zakonshme&action=edit&redlink=1" class="new" title="Ekuacioneve diferenciale të zakonshme (nuk është shkruar akoma)">ekuacioneve diferenciale të zakonshme</a>, metodat spektrale në një hapësire të përshtatshme Hilberti përdoren për të studiuar sjelljen e vlerave të veta dhe "funksioneve të veta" të ekuacioneve diferenciale. Për shembull, <a href="/w/index.php?title=Teoria_e_Sturm%E2%80%93Ljuvilit&action=edit&redlink=1" class="new" title="Teoria e Sturm–Ljuvilit (nuk është shkruar akoma)">problemi i Sturm–Ljuvilit</a> del në studimin e valëve harmonike në një kordë (tel i shtrënguar) ose në një daulle.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Problemi është një ekuacion diferencial i formës </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {d}{dx}}\left[p(x){\frac {dy}{dx}}\right]+q(x)y=\lambda w(x)y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>y</mi> <mo>=</mo> <mi>λ</mi> <mi>w</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {d}{dx}}\left[p(x){\frac {dy}{dx}}\right]+q(x)y=\lambda w(x)y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/602724cf86eeb13a9c5417c7eba4846626dc6623" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.339ex; height:6.176ex;" alt="{\displaystyle -{\frac {d}{dx}}\left[p(x){\frac {dy}{dx}}\right]+q(x)y=\lambda w(x)y}"></span></dd></dl> <p>Për një variabël të panjohur <i>y</i> në një interval [<i>a</i>,<i>b</i>], që kënaq <a href="/w/index.php?title=Konditat_kufitare_homogjene_Robin&action=edit&redlink=1" class="new" title="Konditat kufitare homogjene Robin (nuk është shkruar akoma)">konditat kufitare homogjene Robin</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}\alpha y(a)+\alpha 'y'(a)=0\\\beta y(b)+\beta 'y'(b)=0.\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>α</mi> <mi>y</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>β</mi> <mi>y</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msup> <mi>β</mi> <mo>′</mo> </msup> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}\alpha y(a)+\alpha 'y'(a)=0\\\beta y(b)+\beta 'y'(b)=0.\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc321e8bf14fc02f874e7746cefde742d636ecb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.335ex; height:6.176ex;" alt="{\displaystyle {\begin{cases}\alpha y(a)+\alpha 'y'(a)=0\\\beta y(b)+\beta 'y'(b)=0.\end{cases}}}"></span></dd></dl> <p>Funksionet <i>p</i>, <i>q</i>, dhe <i>w</i> jepen më përpara, dhe problemi është të gjendet një funksion <i>y</i> dhe një konstante λ për të cilën ekuacioni ka një zgjidhje. Problemi ka zgjidhje vetëm për disa vlera të caktuara të λ, të quajtura "vlera të veta" të sistemit, kjo është një rrjedhim i teoremës spektrale për <a href="/w/index.php?title=Operatoret_kompakt&action=edit&redlink=1" class="new" title="Operatoret kompakt (nuk është shkruar akoma)">operatoret kompakt</a> të aplikuar tek <a href="/w/index.php?title=Operatori_integral&action=edit&redlink=1" class="new" title="Operatori integral (nuk është shkruar akoma)">operatori integral</a> i përcaktuar nga <a href="/w/index.php?title=Funksioni_i_Grinit&action=edit&redlink=1" class="new" title="Funksioni i Grinit (nuk është shkruar akoma)">funksioni i Grinit</a> për sistemin. Për me tepër, një rrjedhim tjetër i këtij rezultati të përgjithshëm është se "vlerat e veta" λ të një sistemi mund të vendosen në një varg rritës që tenton në infinit.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ekuacionet_diferenciale_pjesore">Ekuacionet diferenciale pjesore</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=4" title="Redakto pjesën: Ekuacionet diferenciale pjesore" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=4" title="Edit section's source code: Ekuacionet diferenciale pjesore"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Teoria_ergodike">Teoria ergodike</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=5" title="Redakto pjesën: Teoria ergodike" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=5" title="Edit section's source code: Teoria ergodike"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Te_tjera">Te tjera</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=6" title="Redakto pjesën: Te tjera" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=6" title="Edit section's source code: Te tjera"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Percaktime_dhe_shembuj">Percaktime dhe shembuj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=7" title="Redakto pjesën: Percaktime dhe shembuj" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=7" title="Edit section's source code: Percaktime dhe shembuj"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësirat_Euklidiane"><span id="Hap.C3.ABsirat_Euklidiane"></span>Hapësirat Euklidiane</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=8" title="Redakto pjesën: Hapësirat Euklidiane" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=8" title="Edit section's source code: Hapësirat Euklidiane"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësira_e_vargjeve_të_pafundme"><span id="Hap.C3.ABsira_e_vargjeve_t.C3.AB_pafundme"></span>Hapësira e vargjeve të pafundme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=9" title="Redakto pjesën: Hapësira e vargjeve të pafundme" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=9" title="Edit section's source code: Hapësira e vargjeve të pafundme"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësirat_e_Lebesgut"><span id="Hap.C3.ABsirat_e_Lebesgut"></span>Hapësirat e Lebesgut</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=10" title="Redakto pjesën: Hapësirat e Lebesgut" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=10" title="Edit section's source code: Hapësirat e Lebesgut"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësirat_e_Sobolevit"><span id="Hap.C3.ABsirat_e_Sobolevit"></span>Hapësirat e Sobolevit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=11" title="Redakto pjesën: Hapësirat e Sobolevit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=11" title="Edit section's source code: Hapësirat e Sobolevit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësirat_e_Hardit"><span id="Hap.C3.ABsirat_e_Hardit"></span>Hapësirat e Hardit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=12" title="Redakto pjesën: Hapësirat e Hardit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=12" title="Edit section's source code: Hapësirat e Hardit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Shumat_direkte">Shumat direkte</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=13" title="Redakto pjesën: Shumat direkte" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=13" title="Edit section's source code: Shumat direkte"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Produktet_tensoriale">Produktet tensoriale</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=14" title="Redakto pjesën: Produktet tensoriale" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=14" title="Edit section's source code: Produktet tensoriale"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Vetitë"><span id="Vetit.C3.AB"></span>Vetitë</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=15" title="Redakto pjesën: Vetitë" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=15" title="Edit section's source code: Vetitë"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Identiteti_i_Pitagorës"><span id="Identiteti_i_Pitagor.C3.ABs"></span>Identiteti i Pitagorës</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=16" title="Redakto pjesën: Identiteti i Pitagorës" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=16" title="Edit section's source code: Identiteti i Pitagorës"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Jobarazimi_i_Bezelit">Jobarazimi i Bezelit</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=17" title="Redakto pjesën: Jobarazimi i Bezelit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=17" title="Edit section's source code: Jobarazimi i Bezelit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Vetia_e_kompletimit">Vetia e kompletimit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=18" title="Redakto pjesën: Vetia e kompletimit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=18" title="Edit section's source code: Vetia e kompletimit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Identiteti_i_Paralelogramit_dhe_polarizimi">Identiteti i Paralelogramit dhe polarizimi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=19" title="Redakto pjesën: Identiteti i Paralelogramit dhe polarizimi" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=19" title="Edit section's source code: Identiteti i Paralelogramit dhe polarizimi"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Topologjia">Topologjia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=20" title="Redakto pjesën: Topologjia" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=20" title="Edit section's source code: Topologjia"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Përafrimi_më_i_mire"><span id="P.C3.ABrafrimi_m.C3.AB_i_mire"></span>Përafrimi më i mire</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=21" title="Redakto pjesën: Përafrimi më i mire" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=21" title="Edit section's source code: Përafrimi më i mire"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Refleksiviteti">Refleksiviteti</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=22" title="Redakto pjesën: Refleksiviteti" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=22" title="Edit section's source code: Refleksiviteti"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Vargjet_me_konvergjencë_të_dobët"><span id="Vargjet_me_konvergjenc.C3.AB_t.C3.AB_dob.C3.ABt"></span>Vargjet me konvergjencë të dobët</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=23" title="Redakto pjesën: Vargjet me konvergjencë të dobët" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=23" title="Edit section's source code: Vargjet me konvergjencë të dobët"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Bazat_ortonormale">Bazat ortonormale</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=24" title="Redakto pjesën: Bazat ortonormale" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=24" title="Edit section's source code: Bazat ortonormale"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Dimensioni_i_Hilbertit">Dimensioni i Hilbertit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=25" title="Redakto pjesën: Dimensioni i Hilbertit" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=25" title="Edit section's source code: Dimensioni i Hilbertit"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Hapësirat_e_ndashme"><span id="Hap.C3.ABsirat_e_ndashme"></span>Hapësirat e ndashme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=26" title="Redakto pjesën: Hapësirat e ndashme" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=26" title="Edit section's source code: Hapësirat e ndashme"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Komplementi_dhe_projeksioni_ortogonal">Komplementi dhe projeksioni ortogonal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=27" title="Redakto pjesën: Komplementi dhe projeksioni ortogonal" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=27" title="Edit section's source code: Komplementi dhe projeksioni ortogonal"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Operatoret_ne_hapësirat_Hilbertiane"><span id="Operatoret_ne_hap.C3.ABsirat_Hilbertiane"></span>Operatoret ne hapësirat Hilbertiane</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=28" title="Redakto pjesën: Operatoret ne hapësirat Hilbertiane" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=28" title="Edit section's source code: Operatoret ne hapësirat Hilbertiane"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Operatoret_e_lidhur">Operatoret e lidhur</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=29" title="Redakto pjesën: Operatoret e lidhur" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=29" title="Edit section's source code: Operatoret e lidhur"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Operatoret_e_palidhur">Operatoret e palidhur</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=30" title="Redakto pjesën: Operatoret e palidhur" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=30" title="Edit section's source code: Operatoret e palidhur"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Shikoni_gjithashtu">Shikoni gjithashtu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=31" title="Redakto pjesën: Shikoni gjithashtu" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=31" title="Edit section's source code: Shikoni gjithashtu"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul style="border: solid var(--border-color-base, #a2a9b1) 1px; padding: 4px;background-color:var(--background-color-neutral-subtle, #f8f9fa); color: inherit; text-align: center; margin-top: 1em; margin-left: 0; clear: both; list-style:none;"><li style="display: inline;"><a href="/w/index.php?title=Stampa:Portal_Matematika&action=edit&redlink=1" class="new" title="Stampa:Portal Matematika (nuk është shkruar akoma)">Stampa:Portal Matematika</a> </li><li style="display: inline; vertical-align:middle;"><a href="/w/index.php?title=Stampa:Portal_Nuvola_apps_edu_mathematics_blue-p.svg&action=edit&redlink=1" class="new" title="Stampa:Portal Nuvola apps edu mathematics blue-p.svg (nuk është shkruar akoma)">Stampa:Portal Nuvola apps edu mathematics blue-p.svg</a></li><li style="display: inline; vertical-align:middle;"></li><li style="display: inline; vertical-align:middle;"></li><li style="display: inline; vertical-align:middle;"></li><li style="display: inline; vertical-align:middle;"></li><li style="display: inline; vertical-align:middle;"></li></ul> <div class="noprint" style="clear:right; border:solid #aaa 1px; margin:0 0 1em 1em; font-size:90%; background:#f9f9f9; width:250px; padding:4px; spacing:0px; text-align:left; float:right;"> <div style="float:left;"><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/Skeda:Wikibooks-logo-en.svg" class="mw-file-description" title="Wikibooks:Category"><img alt="Wikibooks:Category" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/50px-Wikibooks-logo-en.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/75px-Wikibooks-logo-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Wikibooks-logo-en.svg/100px-Wikibooks-logo-en.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Wikibooks:Category</figcaption></figure></div> <div style="margin-left: 40px;"> <a href="/wiki/Wikibooks" title="Wikibooks">Wikibooks</a> ka më shumë informacione për ketë temë:</div> <div style="margin-left: 10px;"> <i><b><a href="https://sq.wikibooks.org/wiki/Analiza_Funksionale/Hap%C3%ABsirat_e_Hilbertit" class="extiw" title="b:Analiza Funksionale/Hapësirat e Hilbertit">{{{2}}}</a></b></i></div> </div> <ul><li><a href="/wiki/Analiza_harmonike" title="Analiza harmonike">Analiza harmonike</a></li> <li><a href="/w/index.php?title=Operatoret_Hermitiane&action=edit&redlink=1" class="new" title="Operatoret Hermitiane (nuk është shkruar akoma)">Operatoret Hermitiane</a></li> <li><a href="/w/index.php?title=Moduli_Hilbert_C*&action=edit&redlink=1" class="new" title="Moduli Hilbert C* (nuk është shkruar akoma)">Moduli Hilbert C*</a></li> <li><a href="/w/index.php?title=Manifoldi_i_Hilbertit&action=edit&redlink=1" class="new" title="Manifoldi i Hilbertit (nuk është shkruar akoma)">Manifoldi i Hilbertit</a></li> <li><a href="/wiki/Analiza_matematike" class="mw-redirect" title="Analiza matematike">Analiza matematike</a></li> <li><a href="/w/index.php?title=Algjebra_e_operatoreve&action=edit&redlink=1" class="new" title="Algjebra e operatoreve (nuk është shkruar akoma)">Algjebra e operatoreve</a></li> <li><a href="/w/index.php?title=Topologjit%C3%AB_n%C3%AB_nj%C3%AB_bashk%C3%ABsi_t%C3%AB_operatoreve_n%C3%AB_nj%C3%AB_hap%C3%ABsire_Hilberti&action=edit&redlink=1" class="new" title="Topologjitë në një bashkësi të operatoreve në një hapësire Hilberti (nuk është shkruar akoma)">Topologjitë në një bashkësi të operatoreve në një hapësire Hilberti</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Shënime"><span id="Sh.C3.ABnime"></span>Shënime</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=32" title="Redakto pjesën: Shënime" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=32" title="Edit section's source code: Shënime"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-column-count references-column-count-2" style="column-count: 2; -moz-column-count: 2; -webkit-column-count: 2; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">^</a> <span class="reference-text">Shikoni një tekst të <a href="/w/index.php?title=Analiz%C3%ABs&action=edit&redlink=1" class="new" title="Analizës (nuk është shkruar akoma)">analizës</a> me shumë variabla, si <a href="#CITEREFStewart2006">Stewart (2006</a>, Chapter 9).</span> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <span class="reference-text"><a href="#CITEREFBourbaki1987">Bourbaki 1987</a></span> </li> <li id="cite_note-3"><a href="#cite_ref-3">^</a> <span class="reference-text"><a href="#CITEREFSchmidt1907">Schmidt 1907</a>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">^</a> <span class="reference-text"><a href="#CITEREFTitchMarsh1946">TitchMarsh 1946</a>, §IX.1</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">^</a> <span class="reference-text"><a href="#CITEREFLebesgue1904">Lebesgue 1904</a>. Detaje tjera mbi teorinë e integrimit mund të gjenden tek <a href="#CITEREFBourbaki1987">Bourbaki (1987)</a> dhe <a href="#CITEREFSaks2005">Saks (2005)</a>.</span> </li> <li id="cite_note-6"><a href="#cite_ref-6">^</a> <span class="reference-text"><a href="#CITEREFBourbaki1987">Bourbaki 1987</a>.</span> </li> <li id="cite_note-7"><a href="#cite_ref-7">^</a> <span class="reference-text"><a href="#CITEREFDunfordSchwartz1958">Dunford & Schwartz 1958</a>, §IV.16</span> </li> <li id="cite_note-8"><a href="#cite_ref-8">^</a> <span class="reference-text">Në <a href="#CITEREFDunfordSchwartz1958">Dunford & Schwartz (1958</a>, §IV.16), rezultati që çdo funksional linear në L<sup>2</sup>[0,1] i atribuohet <a href="#CITEREFFréchet1907">Fréchet (1907)</a> dhe <a href="#CITEREFRiesz1907">Riesz (1907)</a>. Rezultati i përgjithshëm, që hapësira duale e Hilbertit identifikohet me vete hapësirën e Hilbertit, mund të gjendet tek <a href="#CITEREFRiesz1934">Riesz (1934)</a>.</span> </li> <li id="cite_note-9"><a href="#cite_ref-9">^</a> <span class="reference-text"><a href="#CITEREFvon_Neumann1929">von Neumann 1929</a>.</span> </li> <li id="cite_note-10"><a href="#cite_ref-10">^</a> <span class="reference-text"><a href="#CITEREFHilbertNordheimvon_Neumann1927">Hilbert, Nordheim & von Neumann 1927</a>.</span> </li> <li id="cite_note-Weyl31-11">^ <a href="#cite_ref-Weyl31_11-0"><sup>a</sup></a> <a href="#cite_ref-Weyl31_11-1"><sup>b</sup></a> <span class="reference-text"><a href="#CITEREFWeyl1931">Weyl 1931</a>.</span> </li> <li id="cite_note-12"><a href="#cite_ref-12">^</a> <span class="reference-text"><a href="#CITEREFPrugovečki1981">Prugovečki 1981</a>, pp. 1–10.</span> </li> <li id="cite_note-13"><a href="#cite_ref-13">^</a> <span class="reference-text"><a href="#CITEREFvon_Neumann1932">von Neumann 1932</a></span> </li> <li id="cite_note-14"><a href="#cite_ref-14">^</a> <span class="reference-text"><a href="#CITEREFYoung1987">Young 1987</a>, Chapter 9.</span> </li> <li id="cite_note-15"><a href="#cite_ref-15">^</a> <span class="reference-text">Ajgenvlerat e kernelit të Fredholmit janë 1/λ, të cilat tentojnë në zero.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Referime">Referime</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=33" title="Redakto pjesën: Referime" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=33" title="Edit section's source code: Referime"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r2706204">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFBersJohnSchechter1981" class="citation cs2"><a href="/w/index.php?title=Lipman_Bers&action=edit&redlink=1" class="new" title="Lipman Bers (nuk është shkruar akoma)">Bers, Lipman</a>; <a href="/w/index.php?title=Fritz_John&action=edit&redlink=1" class="new" title="Fritz John (nuk është shkruar akoma)">John, Fritz</a>; Schechter, Martin (1981), <i>Partial differential equations</i>, American Mathematical Society, <a href="/wiki/Speciale:BurimetELibrave/0821800493" class="internal mw-magiclink-isbn">ISBN 0-8218-0049-3</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Partial+differential+equations&rft.pub=American+Mathematical+Society&rft.date=1981&rft.aulast=Bers&rft.aufirst=Lipman&rft.au=John%2C+Fritz&rft.au=Schechter%2C+Martin&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFBourbaki1986" class="citation cs2"><a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Bourbaki, Nicolas</a> (1986), <i>Spectral theories</i>, Elements of mathematics, Berlin: Springer-Verlag, <a href="/wiki/Speciale:BurimetELibrave/0201007673" class="internal mw-magiclink-isbn">ISBN 0-201-00767-3</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spectral+theories&rft.place=Berlin&rft.series=Elements+of+mathematics&rft.pub=Springer-Verlag&rft.date=1986&rft.aulast=Bourbaki&rft.aufirst=Nicolas&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFBourbaki1987" class="citation cs2"><a href="/wiki/Nicolas_Bourbaki" title="Nicolas Bourbaki">Bourbaki, Nicolas</a> (1987), <i>Topological vector spaces</i>, Elements of mathematics, Berlin: Springer-Verlag, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/978-3540136279" title="Speciale:BurimetELibrave/978-3540136279"><bdi>978-3540136279</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Topological+vector+spaces&rft.place=Berlin&rft.series=Elements+of+mathematics&rft.pub=Springer-Verlag&rft.date=1987&rft.isbn=978-3540136279&rft.aulast=Bourbaki&rft.aufirst=Nicolas&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFBrennerScott2005" class="citation cs2">Brenner, S.; Scott, R. L. (2005), <i>The Mathematical Theory of Finite Element Methods</i> (bot. 2nd), Springer, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-3879-5451-1" title="Speciale:BurimetELibrave/0-3879-5451-1"><bdi>0-3879-5451-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematical+Theory+of+Finite+Element+Methods&rft.edition=2nd&rft.pub=Springer&rft.date=2005&rft.isbn=0-3879-5451-1&rft.aulast=Brenner&rft.aufirst=S.&rft.au=Scott%2C+R.+L.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFClarkson1936" class="citation cs2">Clarkson, J. A. (1936), <a rel="nofollow" class="external text" href="http://www.jstor.org/stable/1989630">"Uniformly convex spaces"</a>, <i>Trans. Amer. Math. Soc.</i>, <b>40</b>: 396–414, <a href="https://en.wikipedia.org/wiki/en:doi_(identifier)" class="extiw" title="w:en:doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1989630">10.2307/1989630</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Trans.+Amer.+Math.+Soc.&rft.atitle=Uniformly+convex+spaces&rft.volume=40&rft.pages=396-414&rft.date=1936&rft_id=info%3Adoi%2F10.2307%2F1989630&rft.aulast=Clarkson&rft.aufirst=J.+A.&rft_id=http%3A%2F%2Fwww.jstor.org%2Fstable%2F1989630&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFCourantHilbert1953" class="citation cs2"><a href="/w/index.php?title=Richard_Courant&action=edit&redlink=1" class="new" title="Richard Courant (nuk është shkruar akoma)">Courant, Richard</a>; <a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert, David</a> (1953), <i>Methods of Mathematical Physics, Vol. I</i>, Interscience</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Methods+of+Mathematical+Physics%2C+Vol.+I&rft.pub=Interscience&rft.date=1953&rft.aulast=Courant&rft.aufirst=Richard&rft.au=Hilbert%2C+David&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFDieudonné1960" class="citation cs2"><a href="/w/index.php?title=Jean_Dieudonn%C3%A9&action=edit&redlink=1" class="new" title="Jean Dieudonné (nuk është shkruar akoma)">Dieudonné, Jean</a> (1960), <i>Foundations of Modern Analysis</i>, Academic Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+Modern+Analysis&rft.pub=Academic+Press&rft.date=1960&rft.aulast=Dieudonn%C3%A9&rft.aufirst=Jean&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFDunfordSchwartz1958" class="citation cs2">Dunford, N.; <a href="/w/index.php?title=Jacob_T._Schwartz&action=edit&redlink=1" class="new" title="Jacob T. Schwartz (nuk është shkruar akoma)">Schwartz, J.T.</a> (1958), <i>Linear operators, Parts I and II</i>, Wiley-Interscience</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Linear+operators%2C+Parts+I+and+II&rft.pub=Wiley-Interscience&rft.date=1958&rft.aulast=Dunford&rft.aufirst=N.&rft.au=Schwartz%2C+J.T.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFDuren1970" class="citation cs2">Duren, P. (1970), <i>Theory of H<sup>p</sup>-Spaces</i>, New York: Academic Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+H%3Csup%3Ep%3C%2Fsup%3E-Spaces&rft.place=New+York&rft.pub=Academic+Press&rft.date=1970&rft.aulast=Duren&rft.aufirst=P.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFFolland1989" class="citation cs2">Folland, Gerald B. (1989), <i>Harmonic analysis in phase space</i>, Annals of Mathematics Studies, vëll. 122, Princeton University Press, <a href="/wiki/Speciale:BurimetELibrave/0691085277" class="internal mw-magiclink-isbn">ISBN 0-691-08527-7</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Harmonic+analysis+in+phase+space&rft.series=Annals+of+Mathematics+Studies&rft.pub=Princeton+University+Press&rft.date=1989&rft.aulast=Folland&rft.aufirst=Gerald+B.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFFréchet1907" class="citation cs2">Fréchet, Maurice (1907), "Sur les ensembles de fonctions et les opérations linéaires", <i>C. R. Acad. Sci. Paris</i>, <b>144</b>: 1414–1416</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=C.+R.+Acad.+Sci.+Paris&rft.atitle=Sur+les+ensembles+de+fonctions+et+les+op%C3%A9rations+lin%C3%A9aires&rft.volume=144&rft.pages=1414-1416&rft.date=1907&rft.aulast=Fr%C3%A9chet&rft.aufirst=Maurice&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFFréchet1904–1907" class="citation cs2">Fréchet, Maurice (1904–1907), <i>Sur les opérations linéaires</i></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sur+les+op%C3%A9rations+lin%C3%A9aires&rft.date=1904%2F1907&rft.aulast=Fr%C3%A9chet&rft.aufirst=Maurice&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFGiusti2003" class="citation cs2">Giusti, Enrico (2003), <i>Direct Methods in the Calculus of Variations</i>, World Scientific, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/981-238-043-4" title="Speciale:BurimetELibrave/981-238-043-4"><bdi>981-238-043-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Direct+Methods+in+the+Calculus+of+Variations&rft.pub=World+Scientific&rft.date=2003&rft.isbn=981-238-043-4&rft.aulast=Giusti&rft.aufirst=Enrico&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFHalmos1957" class="citation cs2"><a href="/w/index.php?title=Paul_Halmos&action=edit&redlink=1" class="new" title="Paul Halmos (nuk është shkruar akoma)">Halmos, Paul</a> (1957), <i>Introduction to Hilbert Space and the Theory of Spectral Multiplicity</i>, Chelsea Pub. Co</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Hilbert+Space+and+the+Theory+of+Spectral+Multiplicity&rft.pub=Chelsea+Pub.+Co&rft.date=1957&rft.aulast=Halmos&rft.aufirst=Paul&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFHalmos1982" class="citation cs2"><a href="/w/index.php?title=Paul_Halmos&action=edit&redlink=1" class="new" title="Paul Halmos (nuk është shkruar akoma)">Halmos, Paul</a> (1982), <i>A Hilbert Space Problem Book</i>, Springer-Verlag, <a href="/wiki/Speciale:BurimetELibrave/0387906851" class="internal mw-magiclink-isbn">ISBN 0387906851</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Hilbert+Space+Problem+Book&rft.pub=Springer-Verlag&rft.date=1982&rft.aulast=Halmos&rft.aufirst=Paul&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFHewittStromberg1965" class="citation cs2">Hewitt, Edwin; Stromberg, Karl (1965), <i>Real and Abstract Analysis</i>, New York: Springer-Verlag</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Real+and+Abstract+Analysis&rft.place=New+York&rft.pub=Springer-Verlag&rft.date=1965&rft.aulast=Hewitt&rft.aufirst=Edwin&rft.au=Stromberg%2C+Karl&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFHilbertNordheimvon_Neumann1927" class="citation cs2"><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert, David</a>; <a href="/w/index.php?title=Lothar_Nordheim&action=edit&redlink=1" class="new" title="Lothar Nordheim (nuk është shkruar akoma)">Nordheim, Lothar (Wolfgang)</a>; <a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann, John</a> (1927), <a rel="nofollow" class="external text" href="http://dz-srv1.sub.uni-goettingen.de/sub/digbib/loader?ht=VIEW&did=D27779">"Über die Grundlagen der Quantenmechanik"</a>, <i>Mathematische Annalen</i>, <b>98</b>: 1–30, <a href="https://en.wikipedia.org/wiki/en:doi_(identifier)" class="extiw" title="w:en:doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01451579">10.1007/BF01451579</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=%C3%9Cber+die+Grundlagen+der+Quantenmechanik&rft.volume=98&rft.pages=1-30&rft.date=1927&rft_id=info%3Adoi%2F10.1007%2FBF01451579&rft.aulast=Hilbert&rft.aufirst=David&rft.au=Nordheim%2C+Lothar+%28Wolfgang%29&rft.au=von+Neumann%2C+John&rft_id=http%3A%2F%2Fdz-srv1.sub.uni-goettingen.de%2Fsub%2Fdigbib%2Floader%3Fht%3DVIEW%26did%3DD27779&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="https://en.wikipedia.org/wiki/en:Wikipedia:Link_rot" class="extiw" title="w:en:Wikipedia:Link rot"><span title="">lidhje e vdekur</span></a></i>]</span></sup>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFКолмогоровФомин1989" class="citation cs2"><a href="/w/index.php?title=Andrey_Kolmogorov&action=edit&redlink=1" class="new" title="Andrey Kolmogorov (nuk është shkruar akoma)">Колмогоров, А. Н.</a>; <a href="/w/index.php?title=Sergei_Fomin&action=edit&redlink=1" class="new" title="Sergei Fomin (nuk është shkruar akoma)">Фомин, С. В.</a> (1989), <i>Элементы теории функций и функционального анализа</i> (bot. sixth Russian (with corrections)), "Nauka", Moscow, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/5-02-013993-9" title="Speciale:BurimetELibrave/5-02-013993-9"><bdi>5-02-013993-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D1%8B+%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B8+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B9+%D0%B8+%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D0%BE%D0%B3%D0%BE+%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0&rft.edition=sixth+Russian+%28with+corrections%29&rft.pub=%22Nauka%22%2C+Moscow&rft.date=1989&rft.isbn=5-02-013993-9&rft.aulast=%D0%9A%D0%BE%D0%BB%D0%BC%D0%BE%D0%B3%D0%BE%D1%80%D0%BE%D0%B2&rft.aufirst=%D0%90.+%D0%9D.&rft.au=%D0%A4%D0%BE%D0%BC%D0%B8%D0%BD%2C+%D0%A1.+%D0%92.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFKolmogorovFomin1970" class="citation cs2"><a href="/w/index.php?title=Andrey_Kolmogorov&action=edit&redlink=1" class="new" title="Andrey Kolmogorov (nuk është shkruar akoma)">Kolmogorov, Andrey</a>; <a href="/w/index.php?title=Sergei_Fomin&action=edit&redlink=1" class="new" title="Sergei Fomin (nuk është shkruar akoma)">Fomin, Sergei V.</a> (1970), <i>Introductory Real Analysis</i> (bot. Revised English edition, trans. by Richard A. Silverman (1975)), Dover Press, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-486-61226-0" title="Speciale:BurimetELibrave/0-486-61226-0"><bdi>0-486-61226-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Real+Analysis&rft.edition=Revised+English+edition%2C+trans.+by+Richard+A.+Silverman+%281975%29&rft.pub=Dover+Press&rft.date=1970&rft.isbn=0-486-61226-0&rft.aulast=Kolmogorov&rft.aufirst=Andrey&rft.au=Fomin%2C+Sergei+V.&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFB.M._Levitan" class="citation cs2">B.M. Levitan, <i>Hilbert space</i>, H/h047380</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Hilbert+space&rft.au=B.M.+Levitan&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFReedSimon1980" class="citation cs2"><a href="/w/index.php?title=Michael_Reed&action=edit&redlink=1" class="new" title="Michael Reed (nuk është shkruar akoma)">Reed, Michael</a>; <a href="/w/index.php?title=Barry_Simon&action=edit&redlink=1" class="new" title="Barry Simon (nuk është shkruar akoma)">Simon, Barry</a> (1980), <i>Functional Analysis</i>, Methods of Modern Mathematical Physics, Academic Press, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-12-585050-6" title="Speciale:BurimetELibrave/0-12-585050-6"><bdi>0-12-585050-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Functional+Analysis&rft.series=Methods+of+Modern+Mathematical+Physics&rft.pub=Academic+Press&rft.date=1980&rft.isbn=0-12-585050-6&rft.aulast=Reed&rft.aufirst=Michael&rft.au=Simon%2C+Barry&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFReedSimon1975" class="citation cs2"><a href="/w/index.php?title=Michael_Reed&action=edit&redlink=1" class="new" title="Michael Reed (nuk është shkruar akoma)">Reed, Michael</a>; <a href="/w/index.php?title=Barry_Simon&action=edit&redlink=1" class="new" title="Barry Simon (nuk është shkruar akoma)">Simon, Barry</a> (1975), <i>Fourier Analysis, Self-Adjointness</i>, Methods of Modern Mathematical Physics, Academic Press, <a href="/wiki/Speciale:BurimetELibrave/0125850002" class="internal mw-magiclink-isbn">ISBN 0-12-5850002</a>-6</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fourier+Analysis%2C+Self-Adjointness&rft.series=Methods+of+Modern+Mathematical+Physics&rft.pub=Academic+Press&rft.date=1975&rft.aulast=Reed&rft.aufirst=Michael&rft.au=Simon%2C+Barry&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFPrugovečki1981" class="citation cs2">Prugovečki, Eduard (1981), <i>Quantum mechanics in Hilbert space</i> (bot. 2nd), Dover (publikuar 2006), <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/978-0486453279" title="Speciale:BurimetELibrave/978-0486453279"><bdi>978-0486453279</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantum+mechanics+in+Hilbert+space&rft.edition=2nd&rft.pub=Dover&rft.date=1981&rft.isbn=978-0486453279&rft.aulast=Prugove%C4%8Dki&rft.aufirst=Eduard&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFRiesz1907" class="citation cs2"><a href="/w/index.php?title=Frigyes_Riesz&action=edit&redlink=1" class="new" title="Frigyes Riesz (nuk është shkruar akoma)">Riesz, Frigyes</a> (1907), "Sur une espèce de Géométrie analytique des systèmes de fonctions sommables", <i>C. R. Acad. Sci. Paris</i>, <b>144</b>: 1409–1411</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=C.+R.+Acad.+Sci.+Paris&rft.atitle=Sur+une+esp%C3%A8ce+de+G%C3%A9om%C3%A9trie+analytique+des+syst%C3%A8mes+de+fonctions+sommables&rft.volume=144&rft.pages=1409-1411&rft.date=1907&rft.aulast=Riesz&rft.aufirst=Frigyes&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFRiesz1934" class="citation cs2"><a href="/w/index.php?title=Frigyes_Riesz&action=edit&redlink=1" class="new" title="Frigyes Riesz (nuk është shkruar akoma)">Riesz, Frigyes</a> (1934), "Zur Theorie des Hilbertschen Raumes", <i>Acta Sci. Math. Szeged</i>, <b>7</b>: 34–38</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Sci.+Math.+Szeged&rft.atitle=Zur+Theorie+des+Hilbertschen+Raumes&rft.volume=7&rft.pages=34-38&rft.date=1934&rft.aulast=Riesz&rft.aufirst=Frigyes&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFRieszSz.-Nagy1990" class="citation cs2"><a href="/w/index.php?title=Frigyes_Riesz&action=edit&redlink=1" class="new" title="Frigyes Riesz (nuk është shkruar akoma)">Riesz, Frigyes</a>; <a href="/w/index.php?title=B%C3%A9la_Sz%C5%91kefalvi-Nagy&action=edit&redlink=1" class="new" title="Béla Szőkefalvi-Nagy (nuk është shkruar akoma)">Sz.-Nagy, Béla</a> (1990), <i>Functional analysis</i>, Dover, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-486-66289-6" title="Speciale:BurimetELibrave/0-486-66289-6"><bdi>0-486-66289-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Functional+analysis&rft.pub=Dover&rft.date=1990&rft.isbn=0-486-66289-6&rft.aulast=Riesz&rft.aufirst=Frigyes&rft.au=Sz.-Nagy%2C+B%C3%A9la&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFRudin1973" class="citation cs2"><a href="/w/index.php?title=Walter_Rudin&action=edit&redlink=1" class="new" title="Walter Rudin (nuk është shkruar akoma)">Rudin, Walter</a> (1973), <i>Functional analysis</i>, Tata MacGraw-Hill</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Functional+analysis&rft.pub=Tata+MacGraw-Hill&rft.date=1973&rft.aulast=Rudin&rft.aufirst=Walter&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFSchmidt1908" class="citation cs2"><a href="/w/index.php?title=Erhard_Schmidt&action=edit&redlink=1" class="new" title="Erhard Schmidt (nuk është shkruar akoma)">Schmidt, Erhard</a> (1908), "Über die Auflösung linearer Gleichungen mit unendlich vielen Unbekannten", <i>Rend. Circ. Mat. Palermo</i>, <b>25</b>: 63–77, <a href="https://en.wikipedia.org/wiki/en:doi_(identifier)" class="extiw" title="w:en:doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF03029116">10.1007/BF03029116</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rend.+Circ.+Mat.+Palermo&rft.atitle=%C3%9Cber+die+Aufl%C3%B6sung+linearer+Gleichungen+mit+unendlich+vielen+Unbekannten&rft.volume=25&rft.pages=63-77&rft.date=1908&rft_id=info%3Adoi%2F10.1007%2FBF03029116&rft.aulast=Schmidt&rft.aufirst=Erhard&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFSaks2005" class="citation cs2"><a href="/w/index.php?title=Stanis%C5%82aw_Saks&action=edit&redlink=1" class="new" title="Stanisław Saks (nuk është shkruar akoma)">Saks, Stanisław</a> (2005), <i>Theory of the integral</i> (bot. 2nd Dover), Dover, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/978-0486446486" title="Speciale:BurimetELibrave/978-0486446486"><bdi>978-0486446486</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+the+integral&rft.edition=2nd+Dover&rft.pub=Dover&rft.date=2005&rft.isbn=978-0486446486&rft.aulast=Saks&rft.aufirst=Stanis%C5%82aw&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>; originally published <i>Monografje Matematyczne</i>, vol. 7, Warszawa, 1937.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFStewart2006" class="citation cs2">Stewart, James (2006), <i>Calculus: Concepts and Contexts</i> (bot. 3rd), Thomson/Brooks/Cole</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Concepts+and+Contexts&rft.edition=3rd&rft.pub=Thomson%2FBrooks%2FCole&rft.date=2006&rft.aulast=Stewart&rft.aufirst=James&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFTitchMarsh1946" class="citation cs2"><a href="/w/index.php?title=Edward_Charles_TitchMarsh&action=edit&redlink=1" class="new" title="Edward Charles TitchMarsh (nuk është shkruar akoma)">TitchMarsh, Edward Charles</a> (1946), <i>Eigenfunction expansions, part 1</i>, Oxford University: Clarendon Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Eigenfunction+expansions%2C+part+1&rft.place=Oxford+University&rft.pub=Clarendon+Press&rft.date=1946&rft.aulast=TitchMarsh&rft.aufirst=Edward+Charles&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFvon_Neumann1929" class="citation cs2"><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann, John</a> (1929), "Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren", <i>Mathematische Annalen</i>, <b>102</b>: 49–131, <a href="https://en.wikipedia.org/wiki/en:doi_(identifier)" class="extiw" title="w:en:doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01782338">10.1007/BF01782338</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematische+Annalen&rft.atitle=Allgemeine+Eigenwerttheorie+Hermitescher+Funktionaloperatoren&rft.volume=102&rft.pages=49-131&rft.date=1929&rft_id=info%3Adoi%2F10.1007%2FBF01782338&rft.aulast=von+Neumann&rft.aufirst=John&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFvon_Neumann1932" class="citation cs2"><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann, John</a> (1932), <a rel="nofollow" class="external text" href="http://www.jstor.org/stable/86260">"Physical Applications of the Ergodic Hypothesis"</a>, <i>Proc Natl Acad Sci USA</i>, <b>18</b>: 263–266, <a href="https://en.wikipedia.org/wiki/en:doi_(identifier)" class="extiw" title="w:en:doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.18.3.263">10.1073/pnas.18.3.263</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proc+Natl+Acad+Sci+USA&rft.atitle=Physical+Applications+of+the+Ergodic+Hypothesis&rft.volume=18&rft.pages=263-266&rft.date=1932&rft_id=info%3Adoi%2F10.1073%2Fpnas.18.3.263&rft.aulast=von+Neumann&rft.aufirst=John&rft_id=http%3A%2F%2Fwww.jstor.org%2Fstable%2F86260&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFWalters1982" class="citation cs2">Walters, Peter (1982), <i>An Introduction to Ergodic Theory</i>, Springer-Verlag, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-387-95152-0" title="Speciale:BurimetELibrave/0-387-95152-0"><bdi>0-387-95152-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Ergodic+Theory&rft.pub=Springer-Verlag&rft.date=1982&rft.isbn=0-387-95152-0&rft.aulast=Walters&rft.aufirst=Peter&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFWeyl1931" class="citation cs2"><a href="/w/index.php?title=Hermann_Weyl&action=edit&redlink=1" class="new" title="Hermann Weyl (nuk është shkruar akoma)">Weyl, Hermann</a> (1931), <i>The Theory of Groups and Quantum Mechanics</i> (bot. English 1950), Dover Press, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-486-60269-9" title="Speciale:BurimetELibrave/0-486-60269-9"><bdi>0-486-60269-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Groups+and+Quantum+Mechanics&rft.edition=English+1950&rft.pub=Dover+Press&rft.date=1931&rft.isbn=0-486-60269-9&rft.aulast=Weyl&rft.aufirst=Hermann&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFYoung1988" class="citation cs2">Young, N (1988), <i>An introduction to Hilbert space</i>, Cambridge University Press, <a href="https://en.wikipedia.org/wiki/en:ISBN_(identifier)" class="extiw" title="w:en:ISBN (identifier)">ISBN</a> <a href="/wiki/Speciale:BurimetELibrave/0-521-33071-8" title="Speciale:BurimetELibrave/0-521-33071-8"><bdi>0-521-33071-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+introduction+to+Hilbert+space&rft.pub=Cambridge+University+Press&rft.date=1988&rft.isbn=0-521-33071-8&rft.aulast=Young&rft.aufirst=N&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2706204"><cite id="CITEREFZimmer1990" class="citation cs2"><a href="/w/index.php?title=Robert_Zimmer&action=edit&redlink=1" class="new" title="Robert Zimmer (nuk është shkruar akoma)">Zimmer, Robert</a> (1990), <i>Essential Results of Functional Analysis</i>, University of Chicago Press, <a href="/wiki/Speciale:BurimetELibrave/0226983382" class="internal mw-magiclink-isbn">ISBN 0-226-98338-2</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essential+Results+of+Functional+Analysis&rft.pub=University+of+Chicago+Press&rft.date=1990&rft.aulast=Zimmer&rft.aufirst=Robert&rfr_id=info%3Asid%2Fsq.wikipedia.org%3AHap%C3%ABsira+e+Hilbertit" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Stampa:Citation" title="Stampa:Citation">citation</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Mungon ose është bosh parametri <code class="cs1-code">|language=</code> (<a href="/wiki/Ndihm%C3%AB:Gabimet_CS1#language_missing" title="Ndihmë:Gabimet CS1">Ndihmë!</a>)</span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Lidhje_të_jashtme"><span id="Lidhje_t.C3.AB_jashtme"></span>Lidhje të jashtme</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&veaction=edit&section=34" title="Redakto pjesën: Lidhje të jashtme" class="mw-editsection-visualeditor"><span>Redakto</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hap%C3%ABsira_e_Hilbertit&action=edit&section=34" title="Edit section's source code: Lidhje të jashtme"><span>Redakto nëpërmjet kodit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/HilbertSpace.html">Hilbert Space at Mathworld</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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