Matrix Sylvester equations in the theory of orthogonal polynomials on the unit ...

• Author(s): Branquinho, A. ; Rebocho, M. N.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/11261
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Carathéodory function; Matrix Riccati differential equations; Matrix Sylvester differential equations; Semi-classical functionals; Measures on the unit circle
• Document Type: Preprint
• Language: English

Description

In this paper we characterize sequences of polynomials on the unit circle, orthogonal with respect to a Hermitian linear functional such that its corresponding Carath´eodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of matrix Sylvester differential equations. Furthermore, under certain conditions, we give a representation of such sequences in terms of semi-classical orthogonal polynomials on the unit circle. For the particular case of semi-classical orthogonal polynomials on the unit circle, a characterization in terms of first order differential systems is established. CMUC; Department of Mathematics, University of Coimbra FCT; Fundacão para a Ciência e Tecnologia, SFRH/BD/25426/2005