Algorithms for wavelet construction on Vilenkin groups
type: Item
instance of: scholarly article
title: Algorithms for wavelet construction on Vilenkin groups
zbMATH Open document ID: 1254.42044
DOI: 10.1134/S2070046611030022
author: Evgeny A. Rodionov
author: Yuri A. Farkov
published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications
publication date: 2012-11-13T00:00:00Z
review text: Let \(G_p\) be the \(p\)-adic Vilenkin group. In this paper the authors obtain some algorithms for constructing orthogonal and biorthogonal compactly supported wavelets on \(G_p\). In his series of previous papers [Math. Notes 82, No. 6, 843--859 (2007); translation from Mat. Zametki 82, No. 6, 934--952 (2007; Zbl 1142.42015); J. Approx. Theory 161, No. 1, 259--279 (2009; Zbl 1205.42030); Proc. Steklov Inst. Math. 265, 101--114 (2009); translation from Tr. Mat. Inst. Steklova 265, 110--124 (2009; Zbl 1178.42037)], \textit{Yu. A. Farkov} characterized a refinable function which generates multiresolution analysis in \(L^2(G_p)\) and gives a procedure to construct orthogonal and biorthogonal wavelets in \(L^2(G_p)\). In this procedure the essential part is to solve the problem of completing a unitary matrix with the first row given. The authors give some algorithms to solve this problem.
reviewed by: Takeshi Kawazoe
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 43A70
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 6105075
zbMATH Keywords: orthogonal wavelets
zbMATH Keywords: biorthogonal wavelets
zbMATH Keywords: Vilenkin group
zbMATH Keywords: refinable functions
zbMATH Keywords: Walsh functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6105075