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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 2, Pages 270–280
DOI: https://doi.org/10.17377/smzh.2017.58.203 (Mi smj2858) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On convergence of multiple trigonometric series with monotone coefficients

D. G. Dzhumabaevaa, M. I. Dyachenkob, E. D. Nursultanovc

a Gumilev Eurasian National University, Astana, Kazakhstan
b Lomonosov Moscow State University, Moscow, Russia
c Lomonosov Moscow State University, Kazakhstan Branch, Astana, Kazakhstan
Full-text PDF (307 kB) Citations (3)
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DOI: https://doi.org/10.17377/smzh.2017.58.203
Abstract: We study the Pringsheim pointwise convergence of multiple trigonometric series. We obtain a condition on the coefficients of the series that guarantees its Pringsheim convergence and prove the unimprovability of this condition.
Keywords: multiple trigonometric series, Pringsheim convergence, Lebesgue space with mixed metric, monotone coefficients.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 4080/ГФ4
3311/ГФ4
Russian Foundation for Basic Research 15-01-01236
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
The first author was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant 4080/GF4); the second author was supported by the Russian Foundation for Basic Research (Grant 15-01-01236); and the third author was supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grants 4080/GF4 and 3311/GF4).
Received: 02.02.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 2, Pages 205–214
DOI: https://doi.org/10.1134/S0037446617020033
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 35R30
Language: Russian
Citation: D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Sibirsk. Mat. Zh., 58:2 (2017), 270–280; Siberian Math. J., 58:2 (2017), 205–214
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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