Gabor Frames on Local Fields of Positive Characteristic

Firdous A. Shah

Published 2016-01-20Version 1

Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fi?elds of engineering and science. Finding general and verifi?able 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 ${M_{u(m)b}T_{u(n)a}g:m,n\in \mathbb N_{0}}$ 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.