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Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem

F. Peherstorfer·A. Volberg·P. Yuditskii
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Abstract

First we give here a simple proof of a remarkable result of Videnskii and Shirokov: let $B$ be a Blaschke product with $n$ zeros, then there exists an outer function $\phi, \phi(0)=1$, such that $\|(B\phi)'\| \leq C n$, where $C$ is an absolute constant. Then we apply this result to a certain problem of finding the asymptotic of orthogonal polynomials.

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F. Peherstorfer, A. Volberg, P. Yuditskii. 2005-08-27. Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem. https://arxiv.org/abs/math/0508544

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