Algorithms for wavelet construction on Vilenkin groups

DOI10.1134/S2070046611030022zbMath1254.42044MaRDI QIDQ1760273

Evgeny A. Rodionov, Yuri A. Farkov

Publication date: 13 November 2012

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

zbMATH Keywords

Walsh functionsbiorthogonal waveletsorthogonal waveletsrefinable functionsVilenkin group

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Numerical methods for wavelets (65T60) Analysis on specific locally compact and other abelian groups (43A70)

Related Items (14)

Wavelet frames on Vilenkin groups and their approximation properties ⋮ Biorthogonal wavelets on local fields of positive characteristic ⋮ Wavelet frames related to Walsh functions ⋮ Periodic dyadic wavelets and coding of fractal functions ⋮ Examples of frames on the Cantor dyadic group ⋮ Step refinable functions and orthogonal MRA on Vilenkin groups ⋮ Construction of MRA and non-MRA wavelet sets on Cantor dyadic group ⋮ HAAR BASES FOR $L^2(\mathbb{Q}_2^2)$ GENERATED BY ONE WAVELET FUNCTION ⋮ Periodic wavelets on the \(p\)-adic Vilenkin group ⋮ Characterization of wavelets and MRA wavelets on local fields of positive characteristic ⋮ Discrete wavelet transforms in Walsh analysis ⋮ Nonuniform multiresolution analysis on local fields of positive characteristic ⋮ Wavelet expansions on the Cantor group ⋮ Multiresolution analysis through low-pass filter on local fields of positive characteristic

Cites Work

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• Orthogonal wavelets on direct products of cyclic groups
• On wavelets related to the Walsh series
• Biorthogonal wavelets on Vilenkin groups
• A wavelet theory for local fields and related groups
• Orthogonal wavelets with compact support on locally compact Abelian groups
• Wavelet theory as $ p$-adic spectral analysis
• An algorithm for matrix extension and wavelet construction

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