Abstract
Let α>−1 and Β > −1. Then a function f(x), continuous on the segment [−1; 1], exists such that the sequence of Lagrange interpolation polynomials constructed from the roots of Jacobi polynomials diverges almost everywhere on [−1; 1], and, at the same time, the Fourier-Jacobi series of function f(x) converges uniformly to f(x) on any segment [a; b] ⊂(1; 1).
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Translated from Matematicheskie Zametki, Vol. 20, No. 2, pp. 215–226, August, 1976.
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Privalov, A.A. Lagrange interpolation polynomials and orthogonal Fourier-Jacobi series. Mathematical Notes of the Academy of Sciences of the USSR 20, 679–685 (1976). https://doi.org/10.1007/BF01155874
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DOI: https://doi.org/10.1007/BF01155874