Luef, Franz

Gabor analysis, noncommutative tori and Feichtinger's algebra

in Gabor and wavelet frames World Sci. Publ., Hackensack, NJ Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. Vol.10 (2007) p.77--106, MR2428027

abstract

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
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