A New Approach to Ratio Asymptotics for Orthogonal Polynomials
arXiv:1111.6348
Abstract
We use a non-linear characterization of orthonormal polynomials due to Saff in order to show that the behavior of orthonormal polynomials is determined only by its leading coefficient and its normalization. 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 - one has ratio asymptotics along a sequence of asymptotic density 1.
20 pages, 1 figure. In version 2, Section 3 has been reorganized and presents simpler proofs of the OPRL theorems. Version 3 corrects an error in the statement of Theorem 3.3