Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle
type: Item
instance of: scholarly article
title: Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle
zbMATH Open document ID: 0582.42012
DOI: 10.1007/BF01890022
author: Attila Máté
author: Paul Nevai
author: Vilmos Totik
published in: Constructive Approximation
publication date: 1985-01-01T00:00:00Z
review text: Consider a system \(\{\phi_ n\}\) of polynomials orthonormal on the unit circle with respect to a measure \(d\mu\), with \(\mu '>0\) almost everywhere. Denoting by \(\kappa_ n\) the leading coefficient of \(\phi_ n\), a simple new proof is given for \textit{E. A. Rakhmanov}'s important result that \(\lim_{n\to \infty}\kappa_ n/\kappa_{n+1}=1;\) this result plays a crucial role in extending Szegö's theory about polynomials orthogonal with respect to measures \(d\mu\) with log \(\mu\) '\(\in L^ 1\) to a wider class of orthogonal polynomials.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 3931677
zbMATH Keywords: Szegö's theory
zbMATH Keywords: orthogonal polynomials
MaRDI profile type: Publication
cites work: The Absolute Continuity of Phase Operators
cites work: A class of orthogonal polynomials
cites work: Q4769223
cites work: Remarks on E. A. Rahmanov's paper ''On the asymptotics of the ratio of orthogonal polynomials''
cites work: Q3678152
cites work: Orthogonal polynomials
cites work: On orthogonal polynomials
cites work: Orthogonal Polynomials Defined by a Recurrence Relation
cites work: ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS
cites work: ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS. II
cites work: Q4143689
full work available at URL: https://doi.org/10.1007/bf01890022
OpenAlex ID: W2091142082
description: scientific article; zbMATH DE number 3931677