Asymptotics for Christoffel functions with varying weights
type: Item
instance of: scholarly article
title: Asymptotics for Christoffel functions with varying weights
zbMATH Open document ID: 0970.42016
author: Vilmos Totik
published in: Advances in Applied Mathematics
publication date: 2001-10-03T00:00:00Z
review text: The main result in this paper is the uniform asymptotic behaviour of the Christoffel function \(\lambda_n(w^{2n},x)\) of a varying weight \(w^{2n}\) which is defined on a closed set \(\Sigma\) consisting of a finite number of intervals. This result includes the asymptotics of the Christoffel function for Freud weights, as obtained earlier by \textit{D. S. Lubinsky} [``Strong asymptotics for extremal errors and polynomials associated with Erdős-type weights'' (1989; Zbl 0743.41001)]. Furthermore, it gives the asymptotic distribution of eigenvalues of random matrices (in a strong sense).
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1569404
zbMATH Keywords: Christoffel functions
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: logarithmic potentials
zbMATH Keywords: Freud weights
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
full work available at URL: aama.2000.0698
OpenAlex ID: W2022082326
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DOI: 10.1006/AAMA.2000.0698
description: scientific article; zbMATH DE number 1569404