Mathematical Research Letters

Volume 13, Issue 6, November 2006 pp. 975-983.

Asymptotics of orthogonal polynomials via the Koosis theorem

Authors: F. Nazarov (1), A. Volberg (2), P. Yuditskii (3)
Author institution: Michigan State University (1,2), Bar Ilan University (3)

Summary: The main aim of this short paper is to advertise the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomials for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a Szeg\"o measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Contents Full-Text PDF