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Approximation of continuous functions by the de la Vallée Poussin means for the discrete Fourier-Jacobi sums. (Russian) Zbl 1097.42020

Given an arbitrary continuous function on the interval \([-1,1]\), the author constructs the de la Vallée Poussin-type means for discrete Fourier-Jacobi sums over the orthonormal system of the classical Jacobi polynomials of degree at most \(N\) on the discrete set of the zeros of the Jacobi polynomial of degree \(N\). It is shown 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.
{The paper is identical to [F. M. Korkmasov, Sib. Mat. Zh. 45, No. 2, 334–355 (2004); translation from Sib. Math. J. 45, No. 2, 273–293 (2004; Zbl 1048.42026)].}

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
41A50 Best approximation, Chebyshev systems
41A55 Approximate quadratures

Citations:

Zbl 1048.42026
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