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Mat. Sb. (N.S.), 1981, Volume 114(156), Number 4, Pages 583–610 (Mi msb2356)  

On uniform approximation of functions by Fourier sums

E. A. Sevast'yanov


Abstract: This paper studies traditional problems on uniform approximation of a continuous $2\pi$-periodic function $f$ by its $n$th Fourier sums $S_n(f)$. To this end the deviation $\|f-S_n(f)\|_{C_{2\pi}}$ is estimated in terms of some new functional characteristics. As an application of the estimates a number of known results (due to Lebesgue, Salem, Stechkin, Ul'yanov, Oskolkov, and others) are obtained.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 42:4, 515–538

Bibliographic databases:

UDC: 517.512
MSC: 42A20
Received: 10.08.1979

Citation: E. A. Sevast'yanov, “On uniform approximation of functions by Fourier sums”, Mat. Sb. (N.S.), 114(156):4 (1981), 583–610; Math. USSR-Sb., 42:4 (1982), 515–538

Citation in format AMSBIB
\Bibitem{Sev81}
\by E.~A.~Sevast'yanov
\paper On uniform approximation of functions by Fourier sums
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 114(156)
\issue 4
\pages 583--610
\mathnet{http://mi.mathnet.ru/msb2356}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=615342}
\zmath{https://zbmath.org/?q=an:0487.42003|0476.42002}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 42
\issue 4
\pages 515--538
\crossref{https://doi.org/10.1070/SM1982v042n04ABEH002398}


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