Characterizations of Laguerre-Hahn affine orthogonal polynomials on the unit ci...

• Author(s): Branquinho, A. ; Rebocho, M. N.
• Date: 2007
• Persistent ID: http://hdl.handle.net/10316/11309
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Orthogonal polynomials on the unit circle; Hermitian functionals; Measures on the unit circle; Semi-classical functionals; Carathéodory function
• Document Type: Preprint
• Language: English

Description

In this work we characterize a monic polynomial sequence, orthogonal with respect to a hermitian linear functional u that satisfies a functional equation D(Au) = Bu + zHL, where A,B and H are polynomials and L is the Lebesgue functional, in terms of a first order linear differential equation for the Carath´eodory function associated with u and in terms of a first order structure relation for the orthogonal polynomials. Centro de Matemática da Universidade de Coimbra; INTAS Network Constructive Complex Approximation ref. 03-51-6637; Fundação para a Ciência e Tecnologia, ref. SFRH/BD/25426/2005