Characterizations of Laguerre-Hahn affine orthogonal polynomials on the unit circle
In this Work we characterize a monic polynomial sequence, orthogonal with respect to a hermitian linear functional u that satisfies a functional equation D (An) = Bu + zH L, where A, B and H are polynomials and L is the Lebesgue functional, in terms of a first order linear differential equation for the Caratheodory function associated with u and in terms of a first order structure relation for the orthogonal polynomials.
orthogonal polynomials on the unit circle caratheodory function hermitian functionals measures on the unit circle semi-classical functionals