Tight Wavelet Frame Sets in Finite Vector Spaces

2017/03/20 by Iosevich, Alex, Lai, Chun-Kit, Mayeli, Azita
#FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1703.06842

Abstract

Let q≥ 2 be an integer, and \Bbb F_q^d, d≥ 1, be the vector space over the cyclic space \Bbb F_q. The purpose of this paper is two-fold. First, we obtain sufficient conditions on E ⊂ \Bbb F_q^d such that the inverse Fourier transform of 1_E generates a tight wavelet frame in L²(\Bbb F_q^d). We call these sets (tight) wavelet frame sets. The conditions are given in terms of multiplicative and translational tilings, which is analogous with Theorem 1.1 ([20]) by Wang in the setting of finite fields. In the second part of the paper, we exhibit a constructive method for obtaining tight wavelet frame sets in \Bbb F_q^d, d≥ 2, q an odd prime and q≡ 3 (mod 4).

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