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

Smarzewski, Ryszard; Rutka, Przemysław

doi:10.1090/S0002-9939-09-10150-8

Inequalities of Chernoff type for finite and infinite sequences of classical orthogonal polynomials
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by Ryszard Smarzewski and Przemysław Rutka PDF

Proc. Amer. Math. Soc. 138 (2010), 1305-1315 Request permission

Abstract:

In this paper we present two-sided estimates of Chernoff type for the weighted $L_{w}^{2}$-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.

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