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

2005/08/27 by Franz Peherstorfer, Alexander Volberg, Peherstorfer, F. +3
Mathematics · #42B20 #42C15 #Analytic Number Theory Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical functions and polynomials #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.math/0508544

openalex publication_date 2005/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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