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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

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

This article is cited in 10 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.

UDC: 517.98

Received: 17.07.2003


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

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