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Approximate properties of the de la Vallée Poussin means for the discrete Fourier-Jacobi sums. (Russian, English) Zbl 1048.42026
Sib. Mat. Zh. 45, No. 2, 334-355 (2004); translation in Sib. Math. J. 45, No. 2, 273-293 (2004).
The author considers 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 \([-1,1]\), he constructs the de la Vallée Poussin-type means for discrete Fourier-Jacobi sums over the orthonormal system introduced above. The author proves 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.

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