Asymptotic behavior of Müntz-Christoffel functions at the endpoints
type: Item
instance of: scholarly article
title: Asymptotic behavior of Müntz-Christoffel functions at the endpoints
zbMATH Open document ID: 1186.41010
author: Úlfar F. Stefánsson
published in: Journal of Computational and Applied Mathematics
publication date: 2009-12-18T00:00:00Z
review text: The Müntz polynomials have been applied to several problems in approximation theory: a Müntz type of Gauss-Jacobi quadrature has been developed [\textit{G. V. Milovanovic} and \textit{A. S. Cvetkovic, Aleksandar}, SIAM J. Sci. Comput. 27, No.~3, 893--913 (2005; Zbl 1096.41023)] and the zero distribution of the extremal Müntz polynomials has been investigated [\textit{D. S. Lubinsky} and \textit{E. B. Saff}, Proc. Am. Math. Soc. 135, No.~2, 427--435 (2007; Zbl 1173.41001)]. In the paper, the behavior of Cristoffel functions of different Müntz systems for which the respective exponent sequences are asymptotic is compared. More exactly, using the known asymptotics for the ordinary polynomials, the asymptotic behavior of the Cristoffel functions for Müntz systems for which the exponents are asymptotic to an arithmetic progression is established. The fact that the Cristoffel functions can be written in terms of the orthogonal Müntz polynomials is used.
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 5650083
zbMATH Keywords: Cristoffel functions
zbMATH Keywords: Müntz polynomials
reviewed by: Dan Bărbosu
MaRDI profile type: Publication
full work available at URL: j.cam.2009.02.074
OpenAlex ID: W2141715744
cites work: Q4858543
cites work: Muntz Systems and Orthogonal Muntz-Legendre Polynomials
cites work: Gaussian-type Quadrature Rules for Müntz Systems
cites work: Zero distribution of Müntz extremal polynomials in 𝐿_{𝑝}[0,1]
cites work: Q4861743
cites work: Géza Freud, orthogonal polynomials and Christoffel functions. A case study
cites work: Orthogonal polynomials
DOI: 10.1016/J.CAM.2009.02.074
description: scientific article; zbMATH DE number 5650083