Geodesic
Asymptotics of Orthogonal Polynomials Beyond the Scope of Szeg\H{o}'s Theorem
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 22-32

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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.
Mots-clés : orthogonal polynomial, CMV matrix.
Keywords: extremal problem, Blaschke product 
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A. L. Vol'berg; F. Peherstorfer; P. M. Yuditskii. Asymptotics of Orthogonal Polynomials Beyond the Scope of Szeg\H{o}'s Theorem. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 22-32. http://geodesic.mathdoc.fr/item/FAA_2006_40_4_a2/