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Mat. Zametki, 1968, Volume 3, Issue 5, Pages 587–596 (Mi mz6717)  

This article is cited in 1 scientific paper (total in 1 paper)

Mean approximation of functions by Fourier-Gegenbauer sums

S. Z. Rafal'son

Leningrad Finance and Economics Institute

Abstract: Necessary and sufficient conditions for best approximations of functions in the $L^2_{(1-x^2)^\alpha}(-1,1)$ metric, $-1/2\le\alpha<1/2$ to zero at a certain rate are established (for $\alpha=?1/2$ known results are obtained). Inequalities for algebraic polynomials are used in the reasoning.

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English version:
Mathematical Notes, 1968, 3:5, 374–379

Bibliographic databases:

UDC: 517.5
Received: 15.07.1967

Citation: S. Z. Rafal'son, “Mean approximation of functions by Fourier-Gegenbauer sums”, Mat. Zametki, 3:5 (1968), 587–596; Math. Notes, 3:5 (1968), 374–379

Citation in format AMSBIB
\Bibitem{Raf68}
\by S.~Z.~Rafal'son
\paper Mean approximation of functions by Fourier-Gegenbauer sums
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 5
\pages 587--596
\mathnet{http://mi.mathnet.ru/mz6717}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=227667}
\zmath{https://zbmath.org/?q=an:0199.12402}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 5
\pages 374--379
\crossref{https://doi.org/10.1007/BF01150992}


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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. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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