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In this paper we present two-sided estimates of Chernoff type for the weighted L 2 w -distance of a smooth function to the k-dimensional space of all polynomials of degree less than k, whenever the weight function w solves the Pearson differential equation and generates a finite or infinite sequence of classical orthogonal polynomials. These inequalities are simple corollaries of a unified general theorem, which is the main result of the paper.

Inequalities of Chernoff type for finite and infinite sequences of classical orthogonal polynomials