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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 2(10), Pages 227–244 (Mi msb2672)  

This article is cited in 10 scientific papers (total in 10 papers)

Rational approximation and absolute convergence of Fourier series

E. A. Sevast'yanov


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.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:4, 509–525

Bibliographic databases:

UDC: 517.522.3
MSC: 42A10, 42A28
Received: 06.09.1977

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
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\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/msb2672}
\mathscinet{http://www.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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JJ04900005}


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  • http://mi.mathnet.ru/eng/msb/v149/i2/p227

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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. E. A. Sevast'yanov, “The degree of rational approximation of functions and their differentiability”, Math. USSR-Izv., 17:3 (1981), 595–600  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Math. USSR-Sb., 45:1 (1983), 121–137  mathnet  crossref  mathscinet  zmath
    3. Pekarskii A., “Rational Approximation of the Class Hp, O Greater-Than-P-Greater-Than-Infinity”, Dokl. Akad. Nauk Belarusi, 27:1 (1983), 9–12  mathscinet  isi
    4. V. I. Danchenko, “On separation of singularities of meromorphic functions”, Math. USSR-Sb., 53:1 (1986), 183–201  mathnet  crossref  mathscinet  zmath
    5. E. A. Sevast'yanov, “On an estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions”, Math. USSR-Izv., 26:2 (1986), 347–369  mathnet  crossref  mathscinet  zmath
    6. Danchenko V., “The Estimates of Norms and Variations of Rational Constituents of Meromorphic Functions”, 280, no. 5, 1985, 1043–1046  mathscinet  zmath  isi
    7. A. A. Pekarskii, “Tchebycheff rational approximation in the disk, on the circle, and on a closed interval”, Math. USSR-Sb., 61:1 (1988), 87–102  mathnet  crossref  mathscinet  zmath
    8. Pekarskii A., “Direct and Converse Theorems of Rational Approximation in the Spaces Lp[-1,1] and C[-1,1]”, 293, no. 6, 1987, 1307–1310  mathscinet  isi
    9. A. A. Pekarskii, “Uniform rational approximations and Hardy–Sobolev spaces”, Math. Notes, 56:4 (1994), 1082–1088  mathnet  crossref  mathscinet  zmath  isi
    10. V. I. Danchenko, “Estimates of Green potentials. Applications”, Sb. Math., 194:1 (2003), 63–88  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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