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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 2, Pages 334–355
(Mi smj1073)
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This article is cited in 10 scientific papers (total 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.
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
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https://www.mathnet.ru/eng/smj1073 https://www.mathnet.ru/eng/smj/v45/i2/p334
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