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Sibirsk. Mat. Zh., 2004, Volume 45, Number 2, Pages 334–355 (Mi smj1073)  

This article is cited in 6 scientific papers (total in 6 papers)

Approximate properties of the de la Vallée Poussin means for the discrete Fourier–Jacobi sums

F. M. Korkmasov

Institute of Geothermy Problems

Abstract: We consider the system of the classical Jacobi polynomials of degree at most $N$ which generate an orthogonal system on the discrete set of the zeros of the Jacobi polynomial of degree $N$. Given an arbitrary continuous function on the interval $[-1,1]$, we construct the de la Vallée Poussin-type means for discrete Fourier–Jacobi sums over the orthonormal system introduced above. We prove that, under certain relations between $N$ and the parameters in the definition of de la Vallée Poussin means, the latter approximate a continuous function with the best approximation rate in the space $C[-1,1]$ of continuous functions.

Keywords: Jacobi polynomial, de la Vallée Poussin mean, orthonormal system, discrete set, best approximation, discrete Fourier–Jacobi sum, Christoffel number, Gauss quadrature formula, norm

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English version:
Siberian Mathematical Journal, 2004, 45:2, 273–293

Bibliographic databases:

UDC: 517.98
Received: 17.07.2003

Citation: F. M. Korkmasov, “Approximate properties of the de la Vallée Poussin means for the discrete Fourier–Jacobi sums”, Sibirsk. Mat. Zh., 45:2 (2004), 334–355; Siberian Math. J., 45:2 (2004), 273–293

Citation in format AMSBIB
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\by F.~M.~Korkmasov
\paper Approximate properties of the de la Vall\'ee Poussin means for the discrete Fourier--Jacobi sums
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 2
\pages 334--355
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2061415}
\zmath{https://zbmath.org/?q=an:1048.42026}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 2
\pages 273--293
\crossref{https://doi.org/10.1023/B:SIMJ.0000021284.60159.bd}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220959600008}


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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. F. M. Korkmasov, “O dvumernom analoge ortogonalnykh mnogochlenov Yakobi diskretnogo peremennogo”, Sib. zhurn. vychisl. matem., 10:3 (2007), 277–284  mathnet
    2. A. A. Nurmagomedov, “Convergence of Fourier sums by polynomials orthogonal on arbitrary lattice”, Russian Math. (Iz. VUZ), 56:7 (2012), 52–54  mathnet  crossref  mathscinet
    3. Themistoclakis W., “Uniform Approximation on [-1,1] via Discrete de La Vallee Poussin Means”, Numer. Algorithms, 60:4, SI (2012), 593–612  crossref  mathscinet  zmath  isi  scopus
    4. L. K. Dodunova, A. A. Ageikin, “Approximation of analytic functions by universal Vallee-Poussin sums on the Chebyshev polynomials”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 24 (2018), 12–23  mathnet  crossref
    5. Nurmagomedov A.A., Rasulov N.K., “Two-Sided Estimates of Fourier Sums Lebesgue Functions With Respect to Polynomials Orthogonal on Nonuniform Grids”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 249–259  crossref  mathscinet  isi  scopus
    6. A. A. Nurmagomedov, “Priblizhenie funktsii chastnymi summami ryada Fure po mnogochlenam, ortogonalnym na proizvolnykh setkakh”, Izv. vuzov. Matem., 2020, no. 4, 64–73  mathnet  crossref
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