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We also give applications to a-priori estimates for non-hypoelliptic operators.","publication_date":"2013,,","publication_name":"Functional Analysis and Its Applications","grobid_abstract_attachment_id":"42757008"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On multipliers on compact Lie groups","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [43381039]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div 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class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">On multipliers on 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="43381039" href="https://independent.academia.edu/MichaelRuzhansky"><img alt="Profile image of Michael Ruzhansky" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Michael Ruzhansky</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2013, Functional Analysis and Its Applications</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 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in a compact Lie group","attachmentId":89983158,"attachmentType":"pdf","work_url":"https://www.academia.edu/85216595/Representations_of_the_group_of_functions_taking_values_in_a_compact_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/85216595/Representations_of_the_group_of_functions_taking_values_in_a_compact_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="7" data-entity-id="22082764" 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/22082764/Schatten_classes_and_traces_on_compact_Lie_groups">Schatten classes and traces 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">2013</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we present symbolic criteria for invariant operators on compact topological groups $G$ characterising the Schatten-von Neumann classes $S_{r}(L^{2}(G))$ for all $0<r\leq\infty$. Since it is known that for pseudo-differential operators criteria in terms of kernels may be less effective (Carleman's example), our criteria are given in terms of the operators' symbols defined on the noncommutative analogue of the phase space $G\times\hat{G}$, where $G$ is a compact topological (or Lie) group and $\hat{G}$ is its unitary dual. We also show results concerning general non-invariant operators as well as Schatten properties on Sobolev spaces. A trace formula is derived for operators in the Schatten class $S_{1}(L^{2}(G))$. Examples are given for Bessel potentials associated to sub-Laplacians (sums of squares) on compact Lie groups, as well as for powers of the sub-Laplacian and for other non-elliptic operators on SU(2)$\simeq\mathbb S^3$ and on SO(3).</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":"Schatten classes and traces on compact Lie groups","attachmentId":42756968,"attachmentType":"pdf","work_url":"https://www.academia.edu/22082764/Schatten_classes_and_traces_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/22082764/Schatten_classes_and_traces_on_compact_Lie_groups"><span 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