Tbilisi Mathematical Journal

Gabor frames on local fields of positive characteristic

Firdous A. Shah

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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.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 2 (2016), 129-139.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769073

Digital Object Identifier
doi:10.1515/tmj-2016-0025

Mathematical Reviews number (MathSciNet)
MR3583559

Zentralblatt MATH identifier
1354.42054

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 42C40: Wavelets and other special systems 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 43A70: Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05] 46B15: Summability and bases [See also 46A35]

Keywords
Gabor frame local field Fourier transform

Citation

Shah, Firdous A. Gabor frames on local fields of positive characteristic. Tbilisi Math. J. 9 (2016), no. 2, 129--139. doi:10.1515/tmj-2016-0025. https://projecteuclid.org/euclid.tbilisi/1528769073


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