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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 161–177 (Mi timm1239)  

This article is cited in 1 scientific paper (total in 1 paper)

On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$

N. A. Il'yasov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku

Abstract: A solution of the problem on the exact order of deviation in the uniform metric of partial cubic sums of multiple trigonometric Fourier series on classes of functions with a given majorant for the total modulus of smoothness of the $l$th order in $L_1(\mathbb{T}^{m}) $ is presented, where $l\in \mathbb{N}$, $m\geq 1$.

Keywords: multiple trigonometric Fourier series, partial cubic sums, order of uniform convergence, total modulus of smoothness, exact order of deviation in the uniform metric.

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Bibliographic databases:
UDC: 517.518.475
Received: 09.04.2015

Citation: N. A. Il'yasov, “On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 161–177

Citation in format AMSBIB
\Bibitem{Ily15}
\by N.~A.~Il'yasov
\paper On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 4
\pages 161--177
\mathnet{http://mi.mathnet.ru/timm1239}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468440}
\elib{http://elibrary.ru/item.asp?id=25300995}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Ilyasov, “O poryadke ubyvaniya ravnomernykh modulei gladkosti na klassakh periodicheskikh funktsii $H_{p}^{l}[\omega], l\in \mathbb N, 1\le p<\infty$”, Tr. IMM UrO RAN, 23, no. 4, 2017, 162–175  mathnet  crossref  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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