\(p\)-adic wavelets and their applications
type: Item
instance of: scholarly article
title: \(p\)-adic wavelets and their applications
zbMATH Open document ID: 1308.42031
DOI: 10.1134/S0081543814040129
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-12-17T00:00:00Z
review text: The paper is a survey of the theory of complex-valued wavelet bases on \(p\)-adic spaces and their interpretation as bases of compactly supported eigenvectors of \(p\)-adic pseudodifferential operators. The authors consider the following subjects: construction of \(p\)-adic wavelet bases; connections with the representation theory of \(p\)-adic groups (orbits of functions as wavelet frames); wavelets with matrix dilations; multiresolution analysis and multiresolution wavelet frames; \(p\)-adic Shannon-Kotelnikov theorem. The paper contains a rich list of references on the above topics and related subjects from \(p\)-adic analysis and mathematical physics.
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 6381216
zbMATH Keywords: \(p\)-adic wavelets
zbMATH Keywords: \(p\)-adic pseudodifferential operators
zbMATH Keywords: multiresolution analysis
author: S. V. Kozyrev
author: Andrei Khrennikov
author: V. M. Shelkovich
MaRDI profile type: Publication
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