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Matematicheskie Zametki, 2011, Volume 90, Issue 4, Pages 541–557
DOI: https://doi.org/10.4213/mzm8631 (Mi mzm8631) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Haar System on the Product of Groups of $p$-Adic Integers

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky
Full-text PDF (574 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm8631
Abstract: We present an algorithm for constructing dilation operators on the product of groups of $p$-adic integers and construct a system of Haar functions which is obtained from a single function by using the operations of contraction, translation, and raising to a power. In the two-dimensional case, we describe all the Haar bases.
Keywords: system of Haar functions, the group of $p$-adic integers, wavelet basis, Haar basis, compact group, quotient group, Rademacher function, dilation operator, cyclic subgroup, coset.
Received: 16.12.2009
Revised: 08.11.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 4, Pages 517–532
DOI: https://doi.org/10.1134/S0001434611090239
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: S. F. Lukomskii, “Haar System on the Product of Groups of $p$-Adic Integers”, Mat. Zametki, 90:4 (2011), 541–557; Math. Notes, 90:4 (2011), 517–532
Citation in format AMSBIB
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\paper Haar System on the Product of Groups of~$p$-Adic Integers
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\pages 541--557
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\pages 517--532
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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