Solution of a problem of P. Turán on zeros of orthogonal polynomials on the unit circle
type: Item
instance of: scholarly article
title: Solution of a problem of P. Turán on zeros of orthogonal polynomials on the unit circle
zbMATH Open document ID: 0641.33014
DOI: 10.1016/0021-9045(88)90066-4
author: Luis Vigil
author: María Pilar Alfaro
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: It is well known that the zeros of orthogonal polynomials on the unit circle are all inside the unit circle. \textit{P. Turán} [J. Approximation Theory 29, 23-58 (1980; Zbl 0454.41001)] asked whether there is a system of orthogonal polynomials on the unit circle such that the zeros are everywhere dense in \(\{| z| \leq 1\}\). The authors show, using a straightforward method, that there exist positive measures on the unit circle such that the zeros of the corresponding orthogonal polynomials are dense in \(\{| z| \leq 1\}\), thereby giving an affirmative answer to Turán's problem.
reviewed by: Walter Van Assche
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 4044224
zbMATH Keywords: unit circle
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90066-4
OpenAlex ID: W2001262214
cites work: Q4485522
cites work: Q3270024
cites work: Q3032769
cites work: On some problems connected with polynomials orthogonal on the complex unit circle
cites work: On some open problems of approximation theory
cites work: Q3701918
description: scientific article; zbMATH DE number 4044224