## Gabor frames on local fields of positive characteristic.(English)Zbl 1354.42054

Summary: 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 $$\{M_{u(m)b}T_{u(n)a}g =: \chi_{m}(bx)g(x-u(n)a\}_{m,n\in\mathbb{N}_{0}}$$ 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.

### MSC:

 42C15 General harmonic expansions, frames 42C40 Nontrigonometric harmonic analysis involving 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 46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

### Keywords:

Gabor frame; local field; Fourier transform
Full Text:

### References:

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