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Sbornik: Mathematics, 2012, Volume 203, Issue 9, Pages 1295–1309
DOI: https://doi.org/10.1070/SM2012v203n09ABEH004265
(Mi sm7859)
 

This article is cited in 1 scientific paper (total in 1 paper)

Coefficients of convergent multiple Walsh-Paley series

M. G. Plotnikov

Vologda State Academy of Milk Industry
References:
Abstract: The paper is concerned with the behaviour of the coefficients of multiple Walsh-Paley series that are cube convergent to a finite sum. It is shown that even an everywhere convergent series of this kind may contain coefficients with numbers from a sufficiently large set that grow faster than any preassigned sequence. By Cohen's theorem, this sort of thing cannot happen for multiple trigonometric series that are cube convergent on a set of full measure — their coefficients cannot grow even exponentially. Null subsequences of coefficients are determined for multiple Walsh-Paley series that are cube convergent on a set of definite measure.
Bibliography: 18 titles.
Keywords: multiple Walsh-Paley series, cube convergence, Cantor-Lebesgue theorem.
Received: 02.03.2011 and 19.04.2012
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 9, Pages 67–82
DOI: https://doi.org/10.4213/sm7859
Bibliographic databases:
Document Type: Article
UDC: 517.518
MSC: 42C10, 42B05
Language: English
Original paper language: Russian
Citation: M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Mat. Sb., 203:9 (2012), 67–82; Sb. Math., 203:9 (2012), 1295–1309
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/sm7859
  • https://doi.org/10.1070/SM2012v203n09ABEH004265
  • https://www.mathnet.ru/eng/sm/v203/i9/p67
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:593
    Russian version PDF:192
    English version PDF:12
    References:64
    First page:33
     
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