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On convergence of multiple trigonometric series with monotone coefficients

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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.

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Author information

Authors and Affiliations

  1. Gumilev Eurasian National University, Astana, Kazakhstan

    D. G. Dzhumabaeva

  2. Moscow State University, Moscow, Russia

    M. I. Dyachenko

  3. Kazakh Division, Moscow State University, Astana, Kazakhstan

    E. D. Nursultanov

Authors
  1. D. G. Dzhumabaeva
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  2. M. I. Dyachenko
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  3. E. D. Nursultanov
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Corresponding author

Correspondence to D. G. Dzhumabaeva.

Additional information

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).

Astana; Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 2, pp. 270–280, March–April, 2017; DOI: 10.17377/smzh.2017.58.203.

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Dzhumabaeva, D.G., Dyachenko, M.I. & Nursultanov, E.D. On convergence of multiple trigonometric series with monotone coefficients. Sib Math J 58, 205–214 (2017). https://doi.org/10.1134/S0037446617020033

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  • DOI: https://doi.org/10.1134/S0037446617020033

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