Approximate Properties of the de la Vallee Poussin Means for the Discrete Fourier-Jacobi Sums

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 Vallee 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 Vall'ee Poussin means, the latter approximate a continuous function with the best approximation rate in the space C[-1,1] of continuous functions.