Asymptotics of orthonormal polynomials in the presence of a denumerable set of mass points

Let sigma be a positive measure whose support is an interval E plus a denum erable set of mass points which accumulate at the boundary points of E only . Under the assumptions that the mass points satisfy Blaschke's condition a nd that the absolutely continuous part of sigma satisfies Szego's condition , asymptotics for the orthonormal polynomials on and off the support are gi ven. So far asymptotics were only available if the set of mass points is fi nite.