Asymptotics of orthogonal polynomials via the Koosis theorem

Details Asymptotics of orthogonal polynomials via the Koosis theorem Asymptotics of orthogonal polynomials via the Koosis theorem

2005-10-03

arxiv.org/abs/math-ph/0510012v1

Physics

Mathematical Physics

Scientific paper

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 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.

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