Gabor Analysis, Noncommutative Tori and Feichtinger's algebra

Details Gabor Analysis, Noncommutative Tori and Feichtinger's algebra Gabor Analysis, Noncommutative Tori and Feichtinger's algebra

2005-04-07

arxiv.org/abs/math/0504146v1

IMS Lecture Notes Series 10 (2007)

Mathematics

Functional Analysis

Scientific paper

We 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 Gr\"ochenig 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.

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