Algorithms for wavelet construction on Vilenkin groups
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.
scientific article; zbMATH DE number 6105075