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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 $\sigma_p$.

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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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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
2. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Russian Math. Surveys, 33:4 (1978), 53–117
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