Necessary and Sufficient Condition for an Orthogonal Scaling Function on Vilenkin Groups

DOI10.18500/1816-9791-2019-19-1-24-33zbMath1426.43006OpenAlexW2931790325MaRDI QIDQ5230130

G. S. Berdnikov

Publication date: 20 August 2019

Published in: Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/isu787

zbMATH Keywords

waveletsdirected graphsabelian groupscaling functionMRAVilenkin group

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Analysis on specific locally compact and other abelian groups (43A70)

Cites Work

• Unnamed Item
• Riesz multiresolution analysis on Vilenkin groups
• Step refinable functions and orthogonal MRA on Vilenkin groups
• Orthogonal wavelets on direct products of cyclic groups
• Orthogonal wavelets with compact support on locally compact Abelian groups
• N-Valid trees in wavelet theory on Vilenkin groups
• Biorthogonal dyadic wavelets on $ \mathbb R_+$
• On orthogonal systems of shifts of scaling function on local fields of positive characteristic
• Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases
• Riesz multiresolution analysis on zero-dimensional groups
• Approximation by dyadic wavelets

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