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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
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.
Received: 17.08.2019 Revised: 17.08.2019 Accepted: 19.02.2020
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
Linking options:
https://www.mathnet.ru/eng/smj5998 https://www.mathnet.ru/eng/smj/v61/i3/p513
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Abstract page: | 166 | Full-text PDF : | 83 | References: | 22 | First page: | 3 |
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