A note on orthogonal polynomials
type: Item
instance of: scholarly article
title: A note on orthogonal polynomials
zbMATH Open document ID: 0765.33006
author: Xin Li
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: An important and useful identity in the study of asymptotic properties of orthogonal polynomials is the one stating: \(\int_ 0^{2\pi} z^ k| s_ n(z)|^{-2} d\theta=\int_ 0^{2\pi} z^ k d\mu(\theta)\), \(z=e^{i\theta}\), \(| k|\leq n\), \(n=0,1,2,\dots\), where \(d\mu\) is a finite positive Borel measure on the interval \([0,2\pi]\) with support on an infinite set. The set \(\{s_ n(z)\}_{n=0}^ \infty\) is the unique system of orthonormal polynomials with respect to \(d\mu\) on the unit circle. In this note, the author establishes this identity in a simple and elementary manner.
reviewed by: Peter A. McCoy
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42A99
zbMATH DE Number: 168039
zbMATH Keywords: asymptotic properties
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072707
OpenAlex ID: W2082553172
cites work: Q4009297
cites work: A class of orthogonal polynomials
cites work: Q3270024
cites work: Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle
cites work: ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS. II
cites work: Q4061445
DOI: 10.1216/RMJM/1181072707
description: scientific article; zbMATH DE number 168039