A new approach to ratio asymptotics for orthogonal polynomials

Abstract

We use a non-linear characterization of orthonormal polynomials due to Saff in order to prove an equivalence of norm asymptotics and strong asymptotics for polynomials. Several applications of this equivalence are also discussed. One of our main results is that for regular measures on the closed unit disk - including, but not limited to the unit circle - or the interval [-2,2], one has ratio asymptotics along a sequence of asymptotic density 1.