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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.

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