Weighted Hermite-Fejér interpolation on Laguerre nodes
type: Item
instance of: scholarly article
title: Weighted Hermite-Fejér interpolation on Laguerre nodes
zbMATH Open document ID: 1047.41005
DOI: 10.1023/A:1025187019921
author: Ágota P. Horváth
published in: Acta Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: Let \(w\) be a Laguerre weight function on the halfline \((0,\infty)\). The author introduces weighted Hermite-Fejér interpolation polynomials \(H_{w,n}\) satisfying \(wH_{w,n}=wf\) and \((wH_{w,n})'=0\) at the nodes \(x_1,\dots,x_n\) of a point system. The following convergence result is proved: Let \(\alpha >0\) and \(w(x)=x^\alpha e^{-x}\). If the continuous function \(f\) satisfies \(w(x)f(x) \to 0\) as \(x\to 0\) or \(x\to \infty\), and \(x_1,\dots,x_n\) are the roots of the Laguerre polynomials with parameter \(\alpha -\rho\) for some \(\rho\) with \(0 < \rho <1\) then \(wH_{w,n}\) converges to \(wf\) as \(n \to \infty\) uniformly on the halfline \((0,\infty)\).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 2099110
zbMATH Keywords: weighted Hermite-Fejér interpolation
zbMATH Keywords: normal point systems
zbMATH Keywords: positive operators
zbMATH Keywords: convergence
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
full work available at URL: a:1025187019921
OpenAlex ID: W2036478239
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description: scientific article; zbMATH DE number 2099110