On convergence of multiple trigonometric series with monotone coefficients

D. G. Dzhumabaeva; M. I. Dyachenko; E. D. Nursultanov

doi:10.1134/S0037446617020033

On convergence of multiple trigonometric series with monotone coefficients

Authors: Dzhumabaeva D.G.¹, Dyachenko M.I.², Nursultanov E.D.³
Affiliations:
1. Gumilev Eurasian National University
2. Moscow State University
3. Kazakh Division
Issue: Vol 58, No 2 (2017)
Pages: 205-214
Section: Article
URL: https://journal-vniispk.ru/0037-4466/article/view/171051
DOI: https://doi.org/10.1134/S0037446617020033
ID: 171051

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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.