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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 4, Pages 22–32
DOI: https://doi.org/10.4213/faa850 (Mi faa850) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotics of Orthogonal Polynomials Beyond the Scope of Szegő's Theorem

A. L. Vol'berga, F. Peherstorferb, P. M. Yuditskiibc

a Michigan State University
b Johannes Kepler University Linz
c Bar-Ilan University
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DOI: https://doi.org/10.4213/faa850
Abstract: First, we give a simple proof of a remarkable result due to Videnskii and Shirokov: let $B$ be a Blaschke product with $n$ zeros; then there exists an outer function $\phi$, $\phi(0)=1$, such that $\|(B\phi)'\|\le C n$, where $C$ is an absolute constant. Then we apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.
Keywords: orthogonal polynomial, extremal problem, Blaschke product, CMV matrix.
Received: 15.03.2006
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 4, Pages 264–272
DOI: https://doi.org/10.1007/s10688-006-0043-y
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. L. Vol'berg, F. Peherstorfer, P. M. Yuditskii, “Asymptotics of Orthogonal Polynomials Beyond the Scope of Szegő's Theorem”, Funktsional. Anal. i Prilozhen., 40:4 (2006), 22–32; Funct. Anal. Appl., 40:4 (2006), 264–272
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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