Distributional equation for Laguerre-Hahn functionals on the unit circle

• Autor(es): Branquinho, A. ; Rebocho, M. N.
• Data: 2007
• Identificador Persistente: http://hdl.handle.net/10316/11283
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Hermitian functionals; Measures on the unit circle; Carathéodory function; Laguerre-Hahn affine class on the unit circle; Semi-classical functionals
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carath´eodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F, zAF′ = BF2+CF +D and a distributional equation for u, D(Au) = B1u2+ C1u+H1L, where L is the Lebesgue functional, and the polynomials B1,C1,D1 are defined in terms of the polynomials A,B,C,D CMUC; FCT SFRH/BD/25426/2005