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Matematicheskie Zametki, 2024, Volume 116, Issue 4, Pages 489–503
DOI: https://doi.org/10.4213/mzm14327 (Mi mzm14327) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalized Vilenkin groups

A. M. Vodolazova, M. A. Skopinabc

a Saratov State University
b Saint Petersburg State University
c Regional mathematical center of Southern Federal University, Rostov-on-Don
Full-text PDF (646 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm14327
Abstract: Generalized Vilenkin groups are introduced and studied. To such a group, there corresponds an arbitrary finite Abelian group instead of a cyclic group in the case of classical Vilenkin groups. The foundations of harmonic analysis and methods for constructing wavelets on generalized Vilenkin groups are developed. It is proved that the additive group of any local field of positive characteristic is a generalized Vilenkin group.
Keywords: Vilenkin group, Walsh function, character, $M$-positive set, wavelet system.
Funding agency Grant number
Russian Science Foundation 23-11-00178
The research of the second author was supported by the Russian Science Foundation grant no. 23-11-00178, https://rscf.ru/en/project/23-11-00178/; the results of Secs. 4–6 belong to this author.
Received: 30.03.2024
Revised: 07.05.2024
Published: 11.10.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 4, Pages 588–599
DOI: https://doi.org/10.1134/S0001434624090190
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: A. M. Vodolazov, M. A. Skopina, “Generalized Vilenkin groups”, Mat. Zametki, 116:4 (2024), 489–503; Math. Notes, 116:4 (2024), 588–599
Citation in format AMSBIB
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\by A.~M.~Vodolazov, M.~A.~Skopina
\paper Generalized Vilenkin groups
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 4
\pages 489--503
\mathnet{http://mi.mathnet.ru/mzm14327}
\crossref{https://doi.org/10.4213/mzm14327}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 4
\pages 588--599
\crossref{https://doi.org/10.1134/S0001434624090190}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85213450046}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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