Gabor Analysis, Noncommutative Tori and Feichtinger's algebra

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dc.creatorLuef, Franz
dc.date2005-04-07
dc.date.accessioned2026-07-07T09:27:24Z
dc.date.available2026-07-07T09:27:24Z
dc.descriptionWe point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since the construction of equivalence bimodules for noncommutative tori has a natural formulation in the notions of Gabor analysis. As an application we show that Feichtinger's algebra is such an equivalence bimodule. Furthermore, we present Connes's construction of projective modules for noncommutative tori and the relevance of a generalization of Wiener's lemma for twisted convolution by Gröchenig and Leinert. Finally we indicate an approach to the biorthogonality relation of Wexler-Raz on the existence of dual atoms of a Gabor frame operator based on results about Morita equivalence.
dc.identifierhttps://arxiv.org/abs/math/0504146
dc.identifierhttp://arxiv.org/abs/math/0504146
dc.identifierIMS Lecture Notes Series 10 (2007)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157089
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.titleGabor Analysis, Noncommutative Tori and Feichtinger's algebra
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