Characterizations of Laguerre-Hahn affine orthogonal polynomials on the unit circle

Abstract

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.