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compact Lie groups</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="20410309" href="https://unige-it.academia.edu/SaverioGiulini"><img alt="Profile image of Saverio Giulini" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Saverio Giulini</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1982, Journal of Functional Analysis</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">14 pages</p></div><div 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js-wsj-grid-card-view-pdf" href="https://www.academia.edu/77964879/Central_multiplier_theorems_for_compact_Lie_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="50524891" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50524891/An_Lp_Lq_version_of_Hardys_theorem_for_spherical_Fourier_transform_on_semisimple_Lie_groups">An Lp−Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="169922083" href="https://independent.academia.edu/SlaimBenFarah">Slaim Ben Farah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Mathematics and Mathematical Sciences, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We consider a real semisimple Lie groupGwith finite center andKa maximal compact subgroup ofG. We prove anLp−Lqversion of Hardy&#39;s theorem for the spherical Fourier transform onG. More precisely, leta,bbe positive real numbers,1≤p,q≤∞, andfaK-bi-invariant measurable function onGsuch thatha−1f∈Lp(G)andeb‖λ‖2ℱ(f)∈Lq(𝔞+*)(hais the heat kernel onG). We establish that ifab≥1/4andporqis finite, thenf=0almost everywhere. Ifab&lt;1/4, we prove that for allp,q, there are infinitely many nonzero functionsfand ifab=1/4withp=q=∞, we havef=const ha.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Lp−Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups","attachmentId":68475161,"attachmentType":"pdf","work_url":"https://www.academia.edu/50524891/An_Lp_Lq_version_of_Hardys_theorem_for_spherical_Fourier_transform_on_semisimple_Lie_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50524891/An_Lp_Lq_version_of_Hardys_theorem_for_spherical_Fourier_transform_on_semisimple_Lie_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="74916269" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74916269/A_character_formula_for_the_discrete_series_of_a_semisimple_Lie_group">A character formula for the discrete series of a semisimple Lie group</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="49353112" href="https://independent.academia.edu/JorgeVargas154">Jorge Vargas</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Bulletin of the American Mathematical Society, 1980</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A character formula for the discrete series of a semisimple Lie group","attachmentId":82896748,"attachmentType":"pdf","work_url":"https://www.academia.edu/74916269/A_character_formula_for_the_discrete_series_of_a_semisimple_Lie_group","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74916269/A_character_formula_for_the_discrete_series_of_a_semisimple_Lie_group"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="32615018" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32615018/On_harmonic_analysis_of_spherical_convolutions_on_semisimple_Lie_groups">On harmonic analysis of spherical convolutions on semisimple Lie groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="63277192" href="https://oauife.academia.edu/OlufemiOYADARE">Olufemi OYADARE</a></div><p class="ds-related-work--abstract ds2-5-body-sm">This paper contains a non-trivial generalization of the Harish-Chandra transforms on a connected semisimple Lie group G, with finite center, into what we term spherical convolutions. Among other results we show that its integral over the collection of bounded spherical functions at the identity element e ∈ G is a weighted Fourier transforms of the Abel transform at 0. Being a function on G, the restriction of this integral of its spherical Fourier transforms to the positive-definite spherical functions is then shown to be (the non-zero constant multiple of) a positive-definite distribution on G, which is tempered and invariant on G = SL(2, R). These results suggest the consideration of a calculus on the Schwartz algebras of spherical functions. The Plancherel measure of the spherical convolutions is also explicitly computed.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On harmonic analysis of spherical convolutions on semisimple Lie groups","attachmentId":52787856,"attachmentType":"pdf","work_url":"https://www.academia.edu/32615018/On_harmonic_analysis_of_spherical_convolutions_on_semisimple_Lie_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/32615018/On_harmonic_analysis_of_spherical_convolutions_on_semisimple_Lie_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="22082719" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/22082719/On_multipliers_on_compact_Lie_groups">On multipliers on compact Lie groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="43381039" href="https://independent.academia.edu/MichaelRuzhansky">Michael Ruzhansky</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Functional Analysis and Its Applications, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On multipliers on compact Lie groups","attachmentId":42757008,"attachmentType":"pdf","work_url":"https://www.academia.edu/22082719/On_multipliers_on_compact_Lie_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/22082719/On_multipliers_on_compact_Lie_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="33267607" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/33267607/Series_Analysis_and_Schwartz_Algebras_of_Spherical_Convolutions_on_Semisimple_Lie_Groups">Series Analysis and Schwartz Algebras of Spherical Convolutions on Semisimple Lie Groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="63277192" href="https://oauife.academia.edu/OlufemiOYADARE">Olufemi OYADARE</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We give the exact contributions of Harish-Chandra transform, (Hf)(λ), of Schwartz functions f to the harmonic analysis of spherical convolutions and the corresponding L p − Schwartz algebras on a connected semisimple Lie group G (with finite center). One of our major results gives the proof of how the Trombi-Varadarajan Theorem enters into the spherical convolution transform of L p − Schwartz functions and the generalization of this Theorem under the full spherical convolution map.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Series Analysis and Schwartz Algebras of Spherical Convolutions on Semisimple Lie Groups","attachmentId":53336367,"attachmentType":"pdf","work_url":"https://www.academia.edu/33267607/Series_Analysis_and_Schwartz_Algebras_of_Spherical_Convolutions_on_Semisimple_Lie_Groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/33267607/Series_Analysis_and_Schwartz_Algebras_of_Spherical_Convolutions_on_Semisimple_Lie_Groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="16400216" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/16400216/On_Twisted_Fourier_Analysis_and_Convergence_of_Fourier_Series_on_Discrete_Groups">On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35538661" href="https://uniroma1.academia.edu/RobertoConti">Roberto Conti</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Fourier Analysis and Applications, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups","attachmentId":42500779,"attachmentType":"pdf","work_url":"https://www.academia.edu/16400216/On_Twisted_Fourier_Analysis_and_Convergence_of_Fourier_Series_on_Discrete_Groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/16400216/On_Twisted_Fourier_Analysis_and_Convergence_of_Fourier_Series_on_Discrete_Groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="100799018" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/100799018/ON_THE_DISTRIBUTION_OF_THE_PRINCIPAL_SERIES_IN_L2_r_C7_BY">ON THE DISTRIBUTION OF THE PRINCIPAL SERIES IN L2(r\C7) BY</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="199004770" href="https://independent.academia.edu/MiatelloRoberto">Roberto Miatello</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2013</p><p class="ds-related-work--abstract ds2-5-body-sm">Abstract. Let G be a semisimple Lie group of split rank one with finite center. If T C G is a discrete cocompact subgroup, then L2(V\G) = 2ue6(C)nr(&lt;,&gt;) &apos; &quot; ■ For fixed o G &(M), let P(a) denote the classes of irreducible unitary principal series tra, „ (v e 31*). Let, for s&gt; 0, *¡&gt;a(s) = 2ueP(a)nr(u) ■ esK&quot;, where \a is the eigenvalue of ß (the Casimir element of G) on the class w. In this paper, we determine the singular part of the asymptotic expansion of \¡/a(s) as s- » 0+ if T is torsion free, and the first term of the expansion for arbitrary T. As a consequence, if Na(r) = 2u,E/&gt;(o).pij&lt;/&quot;r(&apos;°) and G is without connected compact normal subgroups, then K(r) ~ Cc ■ \Z(G) DTI- vol(r\C) dim(o) rc (c = {dimG/K), as r- » +00. In the course of the proof, we determine the image and kernel of the restriction homomorphism /*: R(K)- » R(M) between representation rings. Introduction. Let G be a connected, real semisimple Lie group with Lie algebr...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"ON THE DISTRIBUTION OF THE PRINCIPAL SERIES IN L2(r\\C7) BY","attachmentId":101517957,"attachmentType":"pdf","work_url":"https://www.academia.edu/100799018/ON_THE_DISTRIBUTION_OF_THE_PRINCIPAL_SERIES_IN_L2_r_C7_BY","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/100799018/ON_THE_DISTRIBUTION_OF_THE_PRINCIPAL_SERIES_IN_L2_r_C7_BY"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="54535373" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups">On the vector Fourier multipliers for compact groups</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="172262998" href="https://independent.academia.edu/YaoganMensah">Yaogan Mensah</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Open Journal of Mathematical Sciences</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the vector Fourier multipliers for compact groups","attachmentId":70854259,"attachmentType":"pdf","work_url":"https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/54535373/On_the_vector_Fourier_multipliers_for_compact_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":47904943,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":47904943,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_47904943" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="95153984" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/95153984/Discrete_series_for_semisimple_Lie_groups_I_Construction_of_invariant_eigendistributions">Discrete series for semisimple Lie groups I: Construction of invariant eigendistributions</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="236569047" href="https://independent.academia.edu/HarishChandra119">Harish Chandra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Acta Mathematica, 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class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="44110821" href="https://independent.academia.edu/NakhleAsmar">Nakhlé Asmar</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical proceedings of the Cambridge Philosophical Society, 1992</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Harmonic conjugation in L1 on compact abelian groups","attachmentId":112208045,"attachmentType":"pdf","work_url":"https://www.academia.edu/115941011/Harmonic_conjugation_in_L1_on_compact_abelian_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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Ryoo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Cornell University - arXiv, 2022</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Vertical versus horizontal inequalities on simply connected nilpotent Lie groups and groups of polynomial growth","attachmentId":96782243,"attachmentType":"pdf","work_url":"https://www.academia.edu/94281268/Vertical_versus_horizontal_inequalities_on_simply_connected_nilpotent_Lie_groups_and_groups_of_polynomial_growth","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/94281268/Vertical_versus_horizontal_inequalities_on_simply_connected_nilpotent_Lie_groups_and_groups_of_polynomial_growth"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="86207549" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups">On the uniform convergence of Fourier transforms on groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="24490894" href="https://independent.academia.edu/ConstantineGeorgakis">Constantine Georgakis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1970</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the uniform convergence of Fourier transforms on groups","attachmentId":90714653,"attachmentType":"pdf","work_url":"https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/86207549/On_the_uniform_convergence_of_Fourier_transforms_on_groups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="62388452" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/62388452/On_the_Plancherel_measure_for_linear_Lie_groups_of_rank_one">On the Plancherel measure for linear Lie groups of rank one</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="199004770" href="https://independent.academia.edu/MiatelloRoberto">Roberto Miatello</a></div><p class="ds-related-work--metadata ds2-5-body-xs">manuscripta mathematica, 1979</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Plancherel measure for linear Lie groups of rank 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href="https://www.academia.edu/98540864/Lower_bound_of_Riesz_transform_kernels_revisited_and_commutators_on_stratified_Lie_groups">Lower bound of Riesz transform kernels revisited and commutators on stratified Lie groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="261654671" href="https://independent.academia.edu/XuanThinhDuong">Xuan Thinh Duong</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv: Classical Analysis and ODEs, 2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Lower bound of Riesz transform kernels revisited and commutators on stratified Lie 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II</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="63569879" href="https://independent.academia.edu/RichardDMosak">Richard D . Mosak</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1973</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Duality and harmonic analysis on central topological groups. 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href="https://www.academia.edu/21340782/Unitary_representations_of_Lie_groups_and_G_and_x00E5_rding_and_x2019_s_inequality">Unitary representations of Lie groups and G&#x00E5;rding&#x2019;s inequality</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42433526" href="https://collegeview.academia.edu/PalleJorgensen">Palle Jorgensen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the American Mathematical Society, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Unitary representations of Lie groups and G\u0026#x00E5;rding\u0026#x2019;s 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Minchenko</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Selecta Mathematica</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Holonomicity of relative characters and applications to multiplicity bounds for spherical pairs","attachmentId":73148709,"attachmentType":"pdf","work_url":"https://www.academia.edu/59016147/Holonomicity_of_relative_characters_and_applications_to_multiplicity_bounds_for_spherical_pairs","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/59016147/Holonomicity_of_relative_characters_and_applications_to_multiplicity_bounds_for_spherical_pairs"><span 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data-entity-id="3454716" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/3454716/A_generalization_of_maximal_functions_on_compact_semisimple_Lie_groups">A generalization of maximal functions on compact semisimple Lie groups</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="4035439" href="https://itb.academia.edu/HendraGunawan">Hendra Gunawan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Pacific Journal of Mathematics, 1992</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A generalization of maximal functions on compact semisimple Lie 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href="https://www.academia.edu/57644684/On_the_Fourier_transform_of_a_compact_semisimple_Lie_group">On the Fourier transform of a compact semisimple Lie group</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48593044" href="https://independent.academia.edu/NormanWildberger">Norman Wildberger</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of the Australian Mathematical Society, 1994</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Fourier transform of a compact semisimple Lie group","attachmentId":72444921,"attachmentType":"pdf","work_url":"https://www.academia.edu/57644684/On_the_Fourier_transform_of_a_compact_semisimple_Lie_group","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" 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Bagchi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A note on the multipliers and and projective representations of semi-simple Lie groups","attachmentId":96787999,"attachmentType":"pdf","work_url":"https://www.academia.edu/94289191/A_note_on_the_multipliers_and_and_projective_representations_of_semi_simple_Lie_groups","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/94289191/A_note_on_the_multipliers_and_and_projective_representations_of_semi_simple_Lie_groups"><span class="ds2-5-text-link__content">View 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