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Mat. Sb., 2009, Volume 200, Number 7, Pages 107–130 (Mi msb4523)  

This article is cited in 5 scientific papers (total in 5 papers)

Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients

Yu. A. Labych, A. P. Starovoitov

Francisk Skorina Gomel State University

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm4523

Full text: PDF file (676 kB)
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English version:
Sbornik: Mathematics, 2009, 200:7, 1051–1074

Bibliographic databases:

UDC: 517.538.52+517.538.53+517.518.84
MSC: Primary 41A20, 41A25; Secondary 41A21, 41A44
Received: 21.02.2008 and 13.01.2009

Citation: Yu. A. Labych, A. P. Starovoitov, “Trigonometric Padé approximants for functions with regularly decreasing Fourier coefficients”, Mat. Sb., 200:7 (2009), 107–130; Sb. Math., 200:7 (2009), 1051–1074

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
    4. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
    5. Lubinsky D.S., “On Uniform Convergence of Diagonal Multipoint Pade Approximants For Entire Functions”, Constr. Approx., 49:1 (2019), 149–174  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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