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December 2016 Gabor frames on local fields of positive characteristic
Firdous A. Shah
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Tbilisi Math. J. 9(2): 129-139 (December 2016). DOI: 10.1515/tmj-2016-0025

Abstract

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply that the Gabor systems are Gabor frames is among the core problems in time-frequency analysis. In this paper, we give some simple and sufficient conditions that ensure a Gabor system $\left\{M_{u(m)b}T_{u(n)a}g=:\chi_{m}(bx)g\big(x-u(n)a\big)\right\}_{ m,n\in\mathbb N_0}$ to be a frame for $L^2(K)$. The conditions proposed are stated in terms of the Fourier transforms of the Gabor system's generating functions.

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Firdous A. Shah. "Gabor frames on local fields of positive characteristic." Tbilisi Math. J. 9 (2) 129 - 139, December 2016. https://doi.org/10.1515/tmj-2016-0025

Information

Received: 7 January 2016; Accepted: 10 October 2016; Published: December 2016
First available in Project Euclid: 12 June 2018

zbMATH: 1354.42054
MathSciNet: MR3583559
Digital Object Identifier: 10.1515/tmj-2016-0025

Subjects:
Primary: 42C15
Secondary: 42B10, ‎42C40, 43A70, 46B15

Rights: Copyright © 2016 Tbilisi Centre for Mathematical Sciences

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Vol.9 • No. 2 • December 2016
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