Strong Asymptotics of Orthonormal Polynomials with the Aid of Green's Function

Abstract

We give explicit asymptotic representations as well as ratio asymptotics of the orthogonal polynomials with asymptotically periodic reflection coefficients in terms of Green's function. All the limit relations will hold uniformly compact outside the support of the measure of orthogonality. Furthermore, with the help of harmonic measures we will characterize all those sets, i.e., supports of orthogonality measures, where orthogonal polynomials with asymptotically periodic reflection coefficients exist.