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Wiener's lemma for twisted convolution and Gabor frames |
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| Authors: | Karlheinz Grö chenig Michael Leinert |
| Institution: | Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009 ; Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany |
| 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'. |
| Keywords: | Twisted convolution Heisenberg group Wiener's Lemma symmetric group algebra Gabor frame modulation space window design invertibility of operators |
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