Strong asymptotics of orthonormal polynomials with the aid of Green's function

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