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Mat. Zametki, 1970, Volume 8, Issue 4, Pages 431–441 (Mi mz9607)  

This article is cited in 2 scientific papers (total in 2 papers)

Approximation of functions by partial sums of Fourier series in polynomials orthogonal on an interval

V. M. Badkov

Siberian Division, V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR

Abstract: For certain weight functions $p(t)$ and $q(t)$, upper bounds are obtained for the difference between partial sums of Fourier series of a function $f$ with respect to the systems $\sigma_p$ and $\sigma_q$ of polynomials orthogonal on $[-1, 1]$ (a comparison theorem is incidentally proved for the systems $\sigma_p$ and $\sigma_q$). By using these upper bounds, known asymptotic expressions for the Lebesgue function, and an upper bound (for $f\in W^rH^\omega$) of the remainder in a Fourier–Chebyshev series, we establish corresponding results for Fourier series with respect to a system $\sigma_p$.

Full text: PDF file (1138 kB)

English version:
Mathematical Notes, 1970, 8:4, 712–717

Bibliographic databases:

UDC: 517.5
Received: 10.11.1969

Citation: V. M. Badkov, “Approximation of functions by partial sums of Fourier series in polynomials orthogonal on an interval”, Mat. Zametki, 8:4 (1970), 431–441; Math. Notes, 8:4 (1970), 712–717

Citation in format AMSBIB
\Bibitem{Bad70}
\by V.~M.~Badkov
\paper Approximation of functions by partial sums of Fourier series in polynomials orthogonal on an interval
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 4
\pages 431--441
\mathnet{http://mi.mathnet.ru/mz9607}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=283485}
\zmath{https://zbmath.org/?q=an:0209.37202}
\transl
\jour Math. Notes
\yr 1970
\vol 8
\issue 4
\pages 712--717
\crossref{https://doi.org/10.1007/BF01104370}


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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, “Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval”, Math. USSR-Sb., 24:2 (1974), 223–256  mathnet  crossref  mathscinet  zmath
    2. 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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