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Matematicheskie Zametki, 2010, Volume 88, Issue 1, Pages 78–96
DOI: https://doi.org/10.4213/mzm8796 (Mi mzm8796) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series

A. A. Talalyan

Institute of Mathematics, National Academy of Sciences of Armenia
Full-text PDF (531 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm8796
Abstract: It is shown that the main uniqueness properties of a multiple trigonometric series are equivalent to similar properties of the corresponding series with respect to a multiple Haar system with variable coefficients. Uniqueness theorems for multiple trigonometric series are proved under different conditions on the coefficients and on the derivative with respect to random binary nets of the sums of the series resulting from their single integration.
Keywords: differentiation with respect to random binary nets, multiple trigonometric series, multiple Haar system, Fourier series, Lebesgue measure.
Received: 25.01.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 1, Pages 79–96
DOI: https://doi.org/10.1134/S0001434610070084
Bibliographic databases:
Document Type: Article
UDC: 517.52
Language: Russian
Citation: A. A. Talalyan, “Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series”, Mat. Zametki, 88:1 (2010), 78–96; Math. Notes, 88:1 (2010), 79–96
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm8796
  • https://doi.org/10.4213/mzm8796
  • https://www.mathnet.ru/eng/mzm/v88/i1/p78
    • This publication is cited in the following 1 articles:
    1. Talalyan A.A., “Martingales and some integrability criterions for multiple trigonometric series”, J. Contemp. Math. Anal., 47:4 (2012), 182–200  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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