Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)


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
Published electronically: September 26, 2003
MathSciNet review: 2015328
Full-text PDF Free Access

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''.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 22D25, 42C15, 22E25, 47B38, 47C15

Retrieve articles in all journals with MSC (2000): 22D25, 42C15, 22E25, 47B38, 47C15

Additional Information

Karlheinz Gröchenig
Affiliation: Department of Mathematics, The University of Connecticut, Storrs, CT 06269-3009

Michael Leinert
Affiliation: Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany

PII: S 0894-0347(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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia