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Mathematics of the USSR-Sbornik, 1979, Volume 35, Issue 4, Pages 509–525
DOI: https://doi.org/10.1070/SM1979v035n04ABEH001569 (Mi sm2672) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Rational approximation and absolute convergence of Fourier series

E. A. Sevast'yanov
English version PDF (912 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM1979v035n04ABEH001569
Abstract: It is proved that if $R_n(f)$ are the smallest uniform deviations of the $2\pi$-periodic function $f$ from rational trigonometric functions of order at most $n$ then the condition $\sum R_n(f)<\infty$ is an unimprovable condition of the absolute convergence of the trigonometric Fourier series of $f$.
Bibliography: 20 titles.
Received: 06.09.1977
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1978, Volume 107(149), Number 2(10), Pages 227–244
Bibliographic databases:
UDC: 517.522.3
MSC: 42A10, 42A28
Language: English
Original paper language: Russian
Citation: E. A. Sevast'yanov, “Rational approximation and absolute convergence of Fourier series”, Mat. Sb. (N.S.), 107(149):2(10) (1978), 227–244; Math. USSR-Sb., 35:4 (1979), 509–525
Citation in format AMSBIB
\Bibitem{Sev78}
\by E.~A.~Sevast'yanov
\paper Rational approximation and absolute convergence of Fourier series
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 2(10)
\pages 227--244
\mathnet{http://mi.mathnet.ru/sm2672}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=512009}
\zmath{https://zbmath.org/?q=an:0422.42003|0398.42007}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 509--525
\crossref{https://doi.org/10.1070/SM1979v035n04ABEH001569}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JJ04900005}
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  • https://doi.org/10.1070/SM1979v035n04ABEH001569
  • https://www.mathnet.ru/eng/sm/v149/i2/p227
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:585
    Russian version PDF:166
    English version PDF:24
    References:86
     
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