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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 3, Pages 513–527
DOI: https://doi.org/10.33048/smzh.2020.61.303
(Mi smj5998)
 

This article is cited in 2 scientific papers (total in 2 papers)

Absolute convergence of the double fourier–franklin series

G. G. Gevorkyan, M. G. Grigoryan

Yerevan State University
Full-text PDF (495 kB) Citations (2)
References:
Abstract: We prove that, for every $0<\epsilon<1$, there exists a measurable set $E\subset{T=[0},1]^{2}$ with measure $|E|>1-\epsilon$ such that, for all $f\in L^{1}({T})$ and $0<\eta<1$, we can find $\tilde f \in L^{1}({T})$ with $\iint\nolimits_{T}| f(x,y)-\tilde f (x,y)| dxdy\leq\eta$ coinciding with $f(x,y)$ on $E$ whose double Fourier–Franklin series converges absolutely to $f$ almost everywhere on $T$.
Keywords: double Fourier series, Franklin system, absolute convergence.
Funding agency Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia 18-1A074
18-1A148
The authors were supported by the Science Committee of Ministry of Education and Science of the Republic of Armenia (Grants 18-1A074 and 18-1A148).
Received: 17.08.2019
Revised: 17.08.2019
Accepted: 19.02.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 3, Pages 403–416
DOI: https://doi.org/10.1134/S0037446620030039
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 35R30
Language: Russian
Citation: G. G. Gevorkyan, M. G. Grigoryan, “Absolute convergence of the double fourier–franklin series”, Sibirsk. Mat. Zh., 61:3 (2020), 513–527; Siberian Math. J., 61:3 (2020), 403–416
Citation in format AMSBIB
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\by G.~G.~Gevorkyan, M.~G.~Grigoryan
\paper Absolute convergence of the double fourier--franklin series
\jour Sibirsk. Mat. Zh.
\yr 2020
\vol 61
\issue 3
\pages 513--527
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\crossref{https://doi.org/10.33048/smzh.2020.61.303}
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\transl
\jour Siberian Math. J.
\yr 2020
\vol 61
\issue 3
\pages 403--416
\crossref{https://doi.org/10.1134/S0037446620030039}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    References:22
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