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

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

2005-08-27

arxiv.org/abs/math/0508544v1

Mathematics

Functional Analysis

Scientific paper

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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