Convergence of modified Lagrange interpolation to \(L_p\)-functions based on the zeros of orthonormal polynomials with Freud weights
type: Item
instance of: scholarly article
title: Convergence of modified Lagrange interpolation to \(L_p\)-functions based on the zeros of orthonormal polynomials with Freud weights
zbMATH Open document ID: 0902.41003
author: K. Appert
published in: Journal of Approximation Theory
publication date: 1998-12-10T00:00:00Z
review text: Let \(\alpha >0\), \(1<p< \infty\), \(W_Q (x)\) be the Freud weight, and let \(L^*(f) \) denote a modified Lagrange interpolation polynomial to a measurable function \(f\) satisfying \[ {\underset x\in \mathbb{R} {\text{ess sup}}} \bigl| f(x)\bigr | W_Q(x) \bigl(1 + | x| \bigr)^\alpha <\infty. \] The author proves that then with a suitable constant \(\Delta= \Delta (p, \alpha)\) \[ \lim_{n \to\infty} \int^\infty_{-\infty} \biggl[ \bigl| f(x)- L^*_n(f;x) \bigr| W_Q(x) \bigl(1+ | x| \bigr)^{-\Delta} \biggr]^p dx=0. \]
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1197064
zbMATH Keywords: Lagrange interpolation
reviewed by: László Leindler
MaRDI profile type: Publication
full work available at URL: jath.1998.3168
OpenAlex ID: W1997654783
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DOI: 10.1006/JATH.1998.3168
description: scientific article; zbMATH DE number 1197064