RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (1557 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.522.3
MSC: 42A10, 42A28

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/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} 

• http://mi.mathnet.ru/eng/msb2672
• http://mi.mathnet.ru/eng/msb/v149/i2/p227

 SHARE:

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
2. A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Math. USSR-Sb., 45:1 (1983), 121–137
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
4. V. I. Danchenko, “On separation of singularities of meromorphic functions”, Math. USSR-Sb., 53:1 (1986), 183–201
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
6. Danchenko V., “The Estimates of Norms and Variations of Rational Constituents of Meromorphic Functions”, 280, no. 5, 1985, 1043–1046
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
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
9. A. A. Pekarskii, “Uniform rational approximations and Hardy–Sobolev spaces”, Math. Notes, 56:4 (1994), 1082–1088
10. V. I. Danchenko, “Estimates of Green potentials. Applications”, Sb. Math., 194:1 (2003), 63–88
•  Number of views: This page: 354 Full text: 93 References: 39