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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive
Izv. RAN. Ser. Mat., 2015 Volume 79, Issue 1, Pages 153–184 (Mi im8181)
This article is cited in 6 papers

Riesz multiresolution analysis on zero-dimensional groups

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: On zero-dimensional groups wavelet Riesz bases with noncompact support are constructed. For Vilenkin groups a simple algorithm for constructing the scaling function in terms of the trees is obtained.

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

UDC: 517.518+519.688

MSC: 42C40, 43A70, 11R56

Received: 24.10.2013

DOI: 10.4213/im8181


 English version: Izvestiya: Mathematics, 2015, 79:1, 145–176

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© Steklov Math. Inst. of RAS, 2025