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twisted group C * -algebras of discrete groups. For amenable groups, Følner nets give the key to Fejér summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.","publication_date":"2009,,","publication_name":"Journal of Fourier Analysis and Applications","grobid_abstract_attachment_id":"42500779"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On Twisted Fourier Analysis and Convergence of Fourier Series on Discrete Groups","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [35538661]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; 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 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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="73982382" 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/73982382/p_Fourier_algebras_on_compact_groups">p-Fourier algebras on 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="13534588" href="https://independent.academia.edu/HunHeeLee">Hun Hee Lee</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p&gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. 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The Nineteenth International Symposium on Multiple-Valued Logic, 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":"On the characterization of the Fourier spectra of functions defined on an Abelian group","attachmentId":44921429,"attachmentType":"pdf","work_url":"https://www.academia.edu/24592600/On_the_characterization_of_the_Fourier_spectra_of_functions_defined_on_an_Abelian_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-related-work-grid-card-view-pdf" href="https://www.academia.edu/24592600/On_the_characterization_of_the_Fourier_spectra_of_functions_defined_on_an_Abelian_group"><span class="ds2-5-text-link__content">View 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