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Matematicheskie Zametki, 2007, Volume 81, Issue 2, Pages 265–279
DOI: https://doi.org/10.4213/mzm3553 (Mi mzm3553) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On Uniqueness Sets for Multiple Walsh Series

M. G. Plotnikov

Vologda State Academy of Milk Industry
Full-text PDF (538 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm3553
Abstract: We study uniqueness sets for multiple Walsh series under $\rho$-regular (or bounded) convergence in rectangles. We prove that a countable set is a uniqueness set for such a series under this convergence. We construct a class of perfect uniqueness sets for multiple Walsh series under this convergence. We show that the notion of index of a perfect set does not solve the problem of whether this set belongs to the class of uniqueness sets. We note that the results of this paper remain valid for several rearranged multiple Walsh series.
Keywords: multiple Walsh series, $\rho$-regular convergence, uniqueness set ($U$-set), $M$-set, perfect set, Rademacher function.
Received: 24.03.2004
Revised: 21.04.2004
English version:
Mathematical Notes, 2007, Volume 81, Issue 2, Pages 234–246
DOI: https://doi.org/10.1134/S0001434607010269
Bibliographic databases:
UDC: 517.518.3
Language: Russian
Citation: M. G. Plotnikov, “On Uniqueness Sets for Multiple Walsh Series”, Mat. Zametki, 81:2 (2007), 265–279; Math. Notes, 81:2 (2007), 234–246
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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