Pointwise convergence of Lagrange interpolation based at the zeros of orthonormal polynomials with respect to weights on the whole real line
type: Item
instance of: scholarly article
title: Pointwise convergence of Lagrange interpolation based at the zeros of orthonormal polynomials with respect to weights on the whole real line
zbMATH Open document ID: 0653.41002
DOI: 10.1016/0021-9045(87)90037-2
author: Arnold Knopfmacher
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: Under various assumptions on a weight \(W^ 2\), with support \({\mathbb{R}}\), we obtain rates for the pointwise convergence of Lagrange interpolation based at the zeros of the orthonormal polynomials with respect to \(W^ 2\), in the case of a uniformly continuous function f(x). The weights considered include \(W_ m(x)=\exp (-| x|^ m)\), m an even positive integer. The technique used generalizes that of Freud, who considered pointwise convergence of Lagrange interpolation in the case of the Hermite weight. However, even for the Hermite weight, our results refine and extend the upper and lower bounds of Freud. We establish as well, as preliminary results, upper and lower bounds for generalized Lebesgue functions and for absolute values of the orthogonal polynomials associated with \(W^ 2_ m(x)\).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4065571
zbMATH Keywords: weight
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: Hermite weight
zbMATH Keywords: Lebesgue functions
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90037-2
OpenAlex ID: W2009095970
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description: scientific article; zbMATH DE number 4065571