Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle
type: Item
instance of: scholarly article
title: Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle
zbMATH Open document ID: 1196.33006
author: M. N. Rebocho
author: A. Branquinho
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2010-07-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1274896211
review text: The paper is devoted to the study of the orthogonal polynomials on the unit circle, whose corresponding Carathéodory function satisfies a Riccati differential equation with polynomial coefficients. It is established the equivalence between this property and the fact that two matrix sequences (related with the orthogonal polynomials, the associated polynomials of the second kind and the functions of the second kind) satisfy the Sylvester differential equations. In particular, the authors obtain a characterization of the semi-classical orthogonal polynomials on the circle in terms of first order linear differential systems.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 39B42
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5735940
zbMATH Keywords: Carathéodory function
zbMATH Keywords: matrix Riccati differential equations
zbMATH Keywords: matrix Sylvester differential equations
zbMATH Keywords: measures on the unit circle
zbMATH Keywords: semiclassical class
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5735940