Mathematics Faculty Articles

Title

Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity

Document Type

Article

Publication Date

1-1-2015

Publication Title

Journal of Geometric Analysis

Keywords

Gabor systems, HRT conjecture, Hardy fields, Kronecker's theorem

ISSN

1050-6926

Volume

25

Issue/No.

1

First Page

226

Last Page

254

Abstract

We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture holds for finite Gabor systems generated by square-integrable functions with certain behavior at infinity. These functions include functions ultimately decaying faster than any exponential function, as well as square-integrable functions ultimately analytic and whose germs are in a Hardy field that is closed under translations. Two classes of the latter type of functions are the set of square-integrable logarithmico-exponential functions and the set of square-integrable Pfaffian functions. We also prove the HRT conjecture for certain finite Gabor systems generated by positive functions.

Comments

Mathematics Subject Classification

42 46

DOI

10.1007/s12220-013-9423-8

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