Wiener’s lemma for twisted convolution and Gabor frames

Gröchenig, Karlheinz; Leinert, Michael

doi:10.1090/S0894-0347-03-00444-2

Wiener’s lemma for twisted convolution and Gabor frames
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by Karlheinz Gröchenig and Michael Leinert;

J. Amer. Math. Soc. 17 (2004), 1-18

DOI: https://doi.org/10.1090/S0894-0347-03-00444-2

Published electronically: September 26, 2003

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Abstract:

We prove non-commutative versions of Wiener’s Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the “irrational case”.

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