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Wiener's lemma for twisted convolution and Gabor frames


Authors: Karlheinz Gröchenig and Michael Leinert
Journal: J. Amer. Math. Soc. 17 (2004), 1-18
MSC (2000): Primary 22D25, 42C15; Secondary 22E25, 47B38, 47C15
DOI: https://doi.org/10.1090/S0894-0347-03-00444-2
Published electronically: September 26, 2003
MathSciNet review: 2015328
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Karlheinz Gröchenig
Affiliation: Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009
Email: GROCH@MATH.UCONN.EDU

Michael Leinert
Affiliation: Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: LEINERT@MATH.UNI-HEIDELBERG.DE

DOI: https://doi.org/10.1090/S0894-0347-03-00444-2
Keywords: Twisted convolution, Heisenberg group, Wiener's Lemma, symmetric group algebra, Gabor frame, modulation space, window design, invertibility of operators
Received by editor(s): July 1, 2001
Published electronically: September 26, 2003
Additional Notes: The first author acknowledges partial support by the Austrian Science Foundation (FWF) under project no. P14485-MAT
Article copyright: © Copyright 2003 American Mathematical Society

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