On differential equations for orthogonal polynomials on the unit circle

In this paper we characterize sequences of orthogonal polynomials on the unit circle whose corresponding Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of second order matrix differential equations. In the semi-classical case, a characterizatio...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 356; no. 1; pp. 242 - 256
Main Authors Branquinho, A., Rebocho, M.N.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.08.2009
Elsevier
Subjects
Algebra
Carathéodory function
Exact sciences and technology
Fourier analysis
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Measures on the unit circle
Ordinary differential equations
Orthogonal polynomials on the unit circle
Riccati differential equations
Sciences and techniques of general use
Semi-classical functionals
Special functions
Riccati differential equations
Carathéodory function
Orthogonal polynomials on the unit circle
Measures on the unit circle
Semi-classical functionals
Second order
Differential equation
Unit circle
Polynomial equation
Orthogonal polynomial
Functional
Linear equation
Mathematical analysis
Riccati equation
Application
Matrix equation
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Summary:In this paper we characterize sequences of orthogonal polynomials on the unit circle whose corresponding Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of second order matrix differential equations. In the semi-classical case, a characterization in terms of second order linear differential equations with polynomial coefficients is deduced.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.03.008