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Generalized Functions, Volume 1: Properties and Operations
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</script> <script src="/js/view.js?v=_C42r0h9hUiY7WdI7n_pmeH7hE79qf9vcFdDdchBPJk"></script> <script type="text/javascript"> productDetailObj = {"ProductId":35938744,"ProductCode":"CHEL/377.H","Title":"Generalized Functions, Volume 1","Subtitle":"Properties and Operations","AMSFlags":"T1","MSCs":"46Fxx||P","CopyrightYear":"1964","PageCount":"423","CoverType":"H","SeriesCode":"CHEL","Series":"AMS Chelsea Publishing","Subseries":"","ProductClassCode":"BS","Volume":"377","ProductDescription":"\u003Cp\u003E The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green\u0027s function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. 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Functions, Volume 1","FullUrl":"","Sort":1,"YoutubeId":""}],"InstructorsManualFlag":"N","InstructorsSolutionManualFlag":"N","ProductText":[{"TextTypeCode":"READERSHIP","Text":"\u003Cp\u003EGraduate students and research mathematicians interested in \r\nanalysis.\u003C/p\u003E","TextHtml":"\u003Cp\u003EGraduate students and research mathematicians interested in analysis.\u003C/p\u003E","SourceHtml":"","SeqNo":0},{"TextTypeCode":"TEXT_COVER4","Text":"\u003Cp\u003EThe first systematic theory of generalized\r\nfunctions (also known as distributions) was created in the early\r\n1950s, although some aspects were developed much earlier, most notably\r\nin the definition of the Green\u0027s function in mathematics and in the\r\nwork of Paul Dirac on quantum electrodynamics in physics. The\r\nsix-volume collection, \u003Cem\u003EGeneralized Functions\u003C/em\u003E, written by\r\nI. M. Gel\u0026prime;fand and co-authors and published in Russian between\r\n1958 and 1966, gives an introduction to generalized functions and\r\npresents various applications to analysis, PDE, stochastic processes,\r\nand representation theory.\u003C/p\u003E \u003Cp\u003EVolume 1 is devoted to basics of the\r\ntheory of generalized functions. The first chapter contains main\r\ndefinitions and most important properties of generalized functions as\r\nfunctional on the space of smooth functions with compact support. The\r\nsecond chapter talks about the Fourier transform of generalized\r\nfunctions. In Chapter 3, definitions and properties of some important\r\nclasses of generalized functions are discussed; in particular,\r\ngeneralized functions supported on submanifolds of lower dimension,\r\ngeneralized functions associated with quadratic forms, and homogeneous\r\ngeneralized functions are studied in detail. Many simple basic\r\nexamples make this book an excellent place for a novice to get\r\nacquainted with the theory of generalized functions. A long appendix\r\npresents basics of generalized functions of complex variables.\r\n\u003C/p\u003E","TextHtml":"\u003Cp\u003EThe first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green\u0027s function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, \u003Cem\u003EGeneralized Functions\u003C/em\u003E, written by I. M. Gel\u0026prime;fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.\u003C/p\u003E\u003Cp\u003EVolume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables. \u003C/p\u003E","SourceHtml":"","SeqNo":0}],"AllowDeskExamCopyRequest":"N","EstimatedPagesFlag":"N","AddToCartFlag":"Y","DisplayAuthorEditorFlag":"B"}; isbnArray.push({ ProductId: "35938744", RelatedType: "ORIGINAL", ISBN: "978-1-4704-2658-3", CoverType: "H" }); </script> <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <input type="hidden" id="hdnProductCode" name="PersonId" value="CHEL/377.H" /> <div id="loadingPanel" class="productDetailLoadingPanel containedToParent"> <div> <div class="sp sp-3balls"></div> </div> </div> <div id="productDetailAddedToCart" class="productDetailAddedToCartContainer jmodal"> <div id="productDetailAddedToCartLoading" class="productDetailLoadingPanel hideContents"> <div> <div class="sp sp-3balls"></div> </div> </div> <div class="productDetailAddedToCartContainer"> <div class="modalHeaderContainer"> <div class="modalIcon"> </div> </div> <div class="productDetailAddedToCartMessage success"> Item Successfully Added to Cart </div> <div class="productDetailAddedToCartMessage error"> An error was encountered while trying to add the item to the cart. 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class="productDetailDescriptionRow"> <span id="lblSeries" class="productDetailSeries">AMS Chelsea Publishing</span> </div> <div class="productDetailDescriptionRow"> <span id="lblSubseries" class="productDetailSubseries"></span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> Volume: <span id='lblVolume' class='productDetailBookInfoLabel'>377</span>; <span id='lblCopyrightYear' class='productDetailBookInfoLabel'>1964</span><span id='lblPageCount' class='productDetailBookInfoLabel'>; 423 pp</span> </span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> MSC: <span id="lblMSC" class="productDetailBookInfoLabel">Primary 46</span> </span> </div> <span id="lblDescription" class="productDetailDescription"><p>The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, <em>Generalized Functions</em>, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.</p><p>Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables. </p></span> <div id="productDetailReadershipHeader" class="productDetailReadershipHeader">Readership</div> <span class="productDetailReadership"><p>Graduate students and research mathematicians interested in analysis.</p></span> <div class="productDetailIncludedInSetHeader">This item is also available as part of a set:</div> <div id="productDetailIncludedInSetPane" class="productDetailIncludedInSetPane"> <ul id="productDetailIncludedInSetPaneUl"> <li class="productDetailIncludedInSetListItem"> <a href="/view?ProductCode=CHELGELFSET">CHELGELFSET</a> </li> </ul> </div> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Table of Contents</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="TOC" role="tabpanel"> <ul id="productDetailTOCContainer" class="productDetailNoList"> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_0" class="productDetailTOC productDetailLevel0">Chapters</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_1" class="productDetailTOC productDetailLevel1">Chapter I. Definition and simplest properties of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_2" class="productDetailTOC productDetailLevel1">Chapter II. Fourier transforms of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_3" class="productDetailTOC productDetailLevel1">Chapter III. Particular types of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_4" class="productDetailTOC productDetailLevel1">Summary of fundamental definitions and equations of volume I</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_5" class="productDetailTOC productDetailLevel1">Table of Fourier transforms</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_6" class="productDetailTOC productDetailLevel1">Appendix A. Proof of the completeness of the generalized-function space</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_7" class="productDetailTOC productDetailLevel1">Appendix B. Generalized functions of complex variables</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_8" class="productDetailTOC productDetailLevel1">Notes and references to the literature</span> </div> </li> </ul> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Additional Material</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="FILE" role="tabpanel"> <ul id="productDetailFileContainer" class="productDetailNoList"> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_0" class="productDetailFile" href="https://www.ams.org/bookstore/pspdf/chel-377-h-intro.pdf" target="_blank">Introduction</a> </div> </li> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_1" class="productDetailFile" href="https://www.ams.org/bookstore/pspdf/chel-377-h-toc.pdf" target="_blank">Table of Contents</a> </div> </li> </ul> </div> </div> </div> </li> <li class="productDetailAccordionListItem"> <div class="productDetailAccordionHeader"> <div class="productDetailAccordionToggleContainer" onclick="toggleDetailMenuItem(this)" onkeypress="handleKeypressForClick(event)" tabindex="0"> <div class="productDetailAccordionLabel">Requests</div> <div class="productDetailAccordionExpand active"> </div> <div class="productDetailAccordionCollapse"> </div> </div> <div class="productDetailAccordionContent"> <div class="tab-pane" id="REQUEST" role="tabpanel"> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('REVIEW');" onkeypress="handleKeypressForClick(event)">Review Copy</a></span><span class="productDetailRequestDescription"> – for publishers of book reviews</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="getPermissions();" onkeypress="handleKeypressForClick(event)">Permission</a></span><span class="productDetailRequestDescription"> – for use of book, eBook, or Journal content</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('ACCESS');" onkeypress="handleKeypressForClick(event)">Accessibility</a></span><span class="productDetailRequestDescription"> – to request an alternate format of an AMS title</span></div> </div> </div> </div> </li> </ul> </div> <div class="productDetailTwoColumn"> <ul class="productDetailNav productDetailNavTabs productDetailNoList" role="tablist"> <li data-tab-id="DESCRIPTION" class="productDetailAdditionalInfo active" role="presentation" onclick="selectTab('DESCRIPTION');" onkeypress="handleKeypressForClick(event)" tabindex="0">Book Details</li> <li data-tab-id="TOC" role="presentation" class="productDetailAdditionalInfo" onclick="selectTab('TOC');" onkeypress="handleKeypressForClick(event)" tabindex="0">Table of Contents</li> <li data-tab-id="FILE" role="presentation" class="productDetailAdditionalInfo wideTab" onclick="selectTab('FILE');" onkeypress="handleKeypressForClick(event)" tabindex="0">Additional Material</li> <li data-tab-id="REQUEST" role="presentation" class="productDetailAdditionalInfo" onclick="selectTab('REQUEST');" onkeypress="handleKeypressForClick(event)" tabindex="0">Requests</li> </ul> <div class="tab-content productDetailTabContent"> <div class="tab-pane active" id="DESCRIPTION" role="tabpanel"> <div class="productDetailDescriptionRow"> <span id="lblSeries" class="productDetailSeries"><a class='productDetailSeriesLink' href='/CHEL'>AMS Chelsea Publishing</a></span> </div> <div class="productDetailDescriptionRow"> <span id="lblSubseries" class="productDetailSubseries"></span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> Volume: <span id='lblVolume' class='productDetailBookInfoLabel'>377</span>; <span id='lblCopyrightYear' class='productDetailBookInfoLabel'>1964</span><span id='lblPageCount' class='productDetailBookInfoLabel'>; 423 pp</span> </span> </div> <div class="productDetailDescriptionRow"> <span class="productDetailBookInfoLabel"> MSC: <span id="lblMSC" class="productDetailBookInfoLabel">Primary 46</span> </span> </div> <span id="lblDescription" class="productDetailDescription"><p>The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, <em>Generalized Functions</em>, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.</p><p>Volume 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables. </p></span> <div id="productDetailReadershipHeader" class="productDetailReadershipHeader">Readership</div> <span class="productDetailReadership"><p>Graduate students and research mathematicians interested in analysis.</p></span> <div class="productDetailIncludedInSetHeader">This item is also available as part of a set:</div> <div id="productDetailIncludedInSetPane" class="productDetailIncludedInSetPane"> <ul id="productDetailIncludedInSetPaneUl"> <li class="productDetailIncludedInSetListItem"> <a href="/view?ProductCode=CHELGELFSET">CHELGELFSET</a> </li> </ul> </div> </div> <div class="tab-pane" id="TOC" role="tabpanel"> <ul id="productDetailTOCContainer" class="productDetailNoList"> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_0" class="productDetailTOC productDetailLevel0">Chapters</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_1" class="productDetailTOC productDetailLevel1">Chapter I. Definition and simplest properties of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_2" class="productDetailTOC productDetailLevel1">Chapter II. Fourier transforms of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_3" class="productDetailTOC productDetailLevel1">Chapter III. Particular types of generalized functions</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_4" class="productDetailTOC productDetailLevel1">Summary of fundamental definitions and equations of volume I</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_5" class="productDetailTOC productDetailLevel1">Table of Fourier transforms</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_6" class="productDetailTOC productDetailLevel1">Appendix A. Proof of the completeness of the generalized-function space</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_7" class="productDetailTOC productDetailLevel1">Appendix B. Generalized functions of complex variables</span> </div> </li> <li> <div class="productDetailTOCRow"> <span id="lblTOCTitle_8" class="productDetailTOC productDetailLevel1">Notes and references to the literature</span> </div> </li> </ul> </div> <div class="tab-pane" id="FILE" role="tabpanel"> <ul id="productDetailFileContainer" class="productDetailNoList"> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_0" class="productDetailFile" href="https://www.ams.org/bookstore/pspdf/chel-377-h-intro.pdf" target="_blank">Introduction</a> </div> </li> <li> <div class="productDetailFileRow"> <a id="lblFileDisplay_1" class="productDetailFile" href="https://www.ams.org/bookstore/pspdf/chel-377-h-toc.pdf" target="_blank">Table of Contents</a> </div> </li> </ul> </div> <div class="tab-pane" id="REQUEST" role="tabpanel"> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('REVIEW');" onkeypress="handleKeypressForClick(event)">Review Copy</a></span><span class="productDetailRequestDescription"> – for publishers of book reviews</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="getPermissions();" onkeypress="handleKeypressForClick(event)">Permission</a></span><span class="productDetailRequestDescription"> – for use of book, eBook, or Journal content</span></div> <div class="productDetailRequestRow"><span class="productDetailRequestHeader"><a href="#" onclick="requestCopy('ACCESS');" onkeypress="handleKeypressForClick(event)">Accessibility</a></span><span class="productDetailRequestDescription"> – to request an alternate format of an AMS title</span></div> </div> </div> </div> </div> <span class="productDetailCrossSellHeader">You may be interested in...</span> <div id="productDetailCrossSellPane" class="slickContainer productDetailCrossSellPane"> <div class="productDetailCrossSellListItem"> <a href="/view?ProductCode=AMSTEXT/4"> <img id="productDetailImage_0" class="productDetailSmallImage" onerror="replaceImageError(this);" src="https://ebus.ams.org/ProductImages/amstext-4-e-cov-1.jpg" title="Fourier Analysis and Its Applications" style=""> </a> </div> <div class="productDetailCrossSellListItem"> <a href="/view?ProductCode=GSM/102"> <img id="productDetailImage_1" class="productDetailSmallImage" onerror="replaceImageError(this);" src="https://ebus.ams.org/ProductImages/sm-gsm-102-01.jpg" title="Introduction to Fourier Analysis and Wavelets" style=""> </a> </div> <div class="productDetailCrossSellListItem"> <a href="/view?ProductCode=MMONO/220"> <img id="productDetailImage_2" class="productDetailSmallImage" onerror="replaceImageError(this);" src="https://ebus.ams.org/ProductImages/mmono-220-e-cov-1.jpg" title="Selected Topics in Integral Geometry" style=""> </a> </div> </div> <div class="productDetailFooterPane"> <a target="_blank"href="https://www.mathjax.org"> <img title="Powered by MathJax" src="https://www.mathjax.org/badge/badge.gif" border="0" alt="Powered by MathJax" /> </a> </div> </div> <div id="productDetailImageZoomWrapper" class="jmodal productDetailImageZoomModal"> <div class="productDetailImageZoomContainer"> <img id="productDetailImageZoom"/> </div> </div> <div id="productDetailGetPermissionsChooserWrapper" class="jmodal productDetailGetPermissionsChooserModal"> <div class="productDetailGetPermissionsInfo"> Please select which format for which you are requesting permissions. </div> <div class="productDetailGetPermissionsChooserContainer"> </div> </div> <input name="__RequestVerificationToken" type="hidden" value="CfDJ8IxuUvaeZRREi9I41erTZ0uxNziGdYHmCLXeLZL9ysONCJfgyHZxIE5E0qXlgB0ovMms81xRg99GQHm_68Deu4bvQTkF9nSwdfR_ZYk0dsmfJ_-OZa_hzFqNTfR4ty3LEcxTLvFySY0SVft0rcXgVz0" /> <script type="text/javascript"> $(document).ready(function () { initViewPage(); 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