This article is cited in 22 papers

Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: For a locally compact zero-dimensional group $(G,\mathbin{\dot+})$, we build a multiresolution analysis and put forward an algorithm for constructing orthogonal wavelet bases. A special case is indicated when a wavelet basis is generated from a single function through contractions, translations and exponentiations.
Bibliography: 19 titles.

Keywords: zero-dimensional groups, multiresolution analysis, wavelet bases.

UDC: 517.518.34+517.518.36+517.986.62

MSC: Primary 42C40; Secondary 46B15, 42C05, 43A15

Received: 21.05.2009 and 07.07.2009

DOI: 10.4213/sm7580

 English version: Sbornik: Mathematics, 2010, 201:5, 669–691

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