2016
DOI: 10.48550/arxiv.1601.03473
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Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields

A. Iosevich,
A. Liu,
A. Mayeli
et al.

Abstract: In this paper we study how zeros of the Fourier transform of a function f : Z d p → C are related to the structure of the function itself. In particular, we introduce a notion of bandwidth of such functions and discuss its connection with the decomposition of this function into wavelets. Connections of these concepts with the tomography principle and the Nyquist-Shannon sampling theorem are explored.We examine a variety of cases such as when the Fourier transform of the characteristic function of a set E vanis… Show more

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