Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality
type: Item
instance of: scholarly article
title: Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality
zbMATH Open document ID: 1155.33006
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-08-19T00:00:00Z
full work available at URL: http://hdl.handle.net/10016/6559
review text: The authors ``study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form \(e^{-\varphi(x)}\), giving a unified treatment for the so-called Freud (i.e., when \(\varphi\) has polynomial growth at infinity) and Erdös (when \(\varphi\) grows faster than any polynomial at infinity) cases''.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5313900
zbMATH Keywords: Logarithmic potential theory
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: zero location
zbMATH Keywords: asymptotic behavior
author: C. Díaz-Mendoza
author: Ramón Orive
author: H. Pijeira Cabrera
reviewed by: Vladimir L. Makarov
MaRDI profile type: Publication
OpenAlex ID: W2153935696
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cites work: Q4360405
cites work: Weighted approximation with varying weight
DOI: 10.1016/J.JMAA.2008.05.029
description: scientific article; zbMATH DE number 5313900