Asymptotics of orthogonal polynomials via the Koosis theorem

2005/10/03 by Fëdor Nazarov, F. Nazarov, Nazarov, F. +6 · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #math-ph #math.MP #math.SP #msc:30C60 #msc:42B20 #msc:42C15

paper · pdf · doi:10.48550/arxiv.math-ph/0510012

arxiv created 2005/10/03 · arxiv updated 2009/12/01

Abstract

The main aim of this short paper is to advertize 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 Szegö 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.

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