Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity

Authors

Johnny J. Benedetto, University of Maryland at College Park
Abdelkrim Bourouihiya, Nova Southeastern UniversityFollow

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

NSUWorks Citation

Benedetto, Johnny J. and Bourouihiya, Abdelkrim, "Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity" (2015). Mathematics Faculty Articles. 70.
https://nsuworks.nova.edu/math_facarticles/70

DOI

10.1007/s12220-013-9423-8