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Sbornik: Mathematics, 2009, Volume 200, Issue 7, Pages 1051–1074
DOI: https://doi.org/10.1070/SM2009v200n07ABEH004027 (Mi sm4523) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients

Yu. A. Labych, A. P. Starovoitov

Francisk Skorina Gomel State University
English version PDF (490 kB) Citations (14) Russian version article
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DOI: https://doi.org/10.1070/SM2009v200n07ABEH004027
Abstract: Sufficient conditions describing the regular decrease of the coefficients of a Fourier series $f(x)=a_0/2+\sum a_n\cos{kx}$ are found which ensure that the trigonometric Padé approximants $\pi^t_{n,m}(x;f)$ converge to the function $f$ in the uniform norm at a rate which coincides asymptotically with the highest possible one. The results obtained are applied to problems dealing with finding sharp constants for rational approximations.
Bibliography: 31 titles.
Keywords: Fourier series, trigonometric Padé approximants, Padé-Chebyshev approximants, best rational approximations.
Received: 21.02.2008 and 13.01.2009
Bibliographic databases:
UDC: 517.538.52+517.538.53+517.518.84
MSC: Primary 41A20, 41A25; Secondary 41A21, 41A44
Language: English
Original paper language: Russian
Citation: Yu. A. Labych, A. P. Starovoitov, “Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients”, Sb. Math., 200:7 (2009), 1051–1074
Citation in format AMSBIB
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\by Yu.~A.~Labych, A.~P.~Starovoitov
\paper Trigonometric Pad\'e approximants for functions with regularly
decreasing Fourier coefficients
\jour Sb. Math.
\yr 2009
\vol 200
\issue 7
\pages 1051--1074
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  • https://doi.org/10.1070/SM2009v200n07ABEH004027
  • https://www.mathnet.ru/eng/sm/v200/i7/p107
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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