Encontrados 6 documentos, a visualizar página 1 de 1

On the semiclassical character of orthogonal polynomials satisfying structure r...

Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ([mu]0,[mu]1) is a coherent pair of measures on the unit circle, then [mu]0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with [mu]1 is a specific rational...

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 Carath´eodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of second order matrix differential equations. ; CMUC, Department of Mathematics, University of Coimbra; FCT, Fundação para a Ciência e Tecnologia SFRH/BD/25426/2005.

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

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-classic...

Distributional equation for Laguerre-Hahn functionals on the unit circle

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 p...

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

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 poly...