Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem
F. Peherstorfer, A. Volberg, P. Yuditskii
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 ϕ, ϕ(0)=1, such that \|(Bϕ)'\| ≤ 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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