On approximation by tight wavelet frames on Vilenkin groups

2023/12/05 by Lukomskii, Sergey, Kruss, Iuliia, Vodolazov, Alexandr
#42C15 #42C40 #FOS: Mathematics #Functional Analysis (math.FA) #G.1 #G.2

paper · doi:10.48550/arxiv.2312.10066

Abstract

We consider the approximate properties of tight wavelet frames on Vilenkin group G. Let \G_n\_{n∈ ℤ} be a main chain of subgroups, X be a set of characters. We define a step function λ(χ) that is constant on cosets G_n^\bot∖G_n-1^\bot by equalities λ(G_n^\bot∖G_n-1^\bot)=λ_n>0 for which ∑(1)/(λ_n)<∞. We find the order of approximation of functions f for which ∫_X|λ( χ)f(χ)|²dν(χ)<∞. As a corollary, we obtain an approximation error for functions from Sobolev spaces with logarithmic weight.

Related

• Wavelet frames on Vilenkin groups and their approximation properties
• On approximation by tight wavelet frames on the field of p-adic numbers
• Wavelet Sets and Generalized Scaling Sets on Vilenkin Group
• Characterization of the pseudo-scaling functions on Vilenkin group
• A characterization of wavelet sets on Vilenkin groups with its application to construction of MRA wavelets