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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the finite linear independence of lattice Gabor systems


Authors: Ciprian Demeter and S. Zubin Gautam
Journal: Proc. Amer. Math. Soc. 141 (2013), 1735-1747
MSC (2010): Primary 42C40, 42B99, 26B99; Secondary 46B15
Published electronically: November 29, 2012
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Abstract: In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell's theorem on the finite linear independence of lattice Gabor systems in $ L^2(\mathbb{R}^d)$. Our proof is based on a simple argument from the spectral theory of random Schrödinger operators; in the one-dimensional setting, we recover the full strength of Linnell's result for general lattices.


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Additional Information

Ciprian Demeter
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: demeterc@indiana.edu

S. Zubin Gautam
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Address at time of publication: School of Law, University of California, Berkeley, California 94720
Email: sgautam@indiana.edu, sgautam@berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11452-2
PII: S 0002-9939(2012)11452-2
Keywords: Gabor systems, HRT Conjecture, random Schrödinger operators
Received by editor(s): December 26, 2010
Received by editor(s) in revised form: September 13, 2011
Published electronically: November 29, 2012
Additional Notes: The first author is supported by a Sloan Research Fellowship and by NSF Grant DMS-0901208.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.