Extensions of Szegö's theory of orthogonal polynomials. II
type: Item
instance of: scholarly article
title: Extensions of Szegö's theory of orthogonal polynomials. II
zbMATH Open document ID: 0635.42023
DOI: 10.1007/BF01890553
author: Attila Máté
author: Paul Nevai
author: Vilmos Totik
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: [For part I see the second author, Lect. Notes Math. 1171, 230-238 (1985; Zbl 0591.42016)]. Let \(d\mu\) be a finite positive measure on the unit circle in the complex plane and \(\{\phi_ n(D\mu)\}\) be a system of orthonormal polynomials on the unit circle with respect to a measure \(d\mu\). If supp(d\(\mu)\) is an infinite set then \(d\mu\) is a distribution. Szegö's theory of orthogonal polynomials is concerned with the asymptotic behavior of \(\phi_ n(d\mu)\) when log \(\mu\) '\(\in L^ 1.\) The authors study the asymptotic behavior of the fraction \(\phi_ n(d\mu_ 1)/\phi_ n(d\mu_ 2)\) outside the unit circle. The consequences for orthogonal polynomials on the real line are also discussed. A few printing mistakes are there in the text.
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 41A60
zbMATH DE Number: 4034333
zbMATH Keywords: Poisson integral
zbMATH Keywords: Riemann integration
zbMATH Keywords: Szegö's theory
zbMATH Keywords: asymptotic behavior
reviewed by: Ajendra Nath Srivastava
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01890553
OpenAlex ID: W4234104450
description: scientific article; zbMATH DE number 4034333