Asymptotics of orthogonal polynomials beyond the scope of Szegő's theorem (Q883699)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotics of orthogonal polynomials beyond the scope of Szegő's theorem |
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Asymptotics of orthogonal polynomials beyond the scope of Szegő's theorem (English)
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8 June 2007
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The authors consider the following result due to Videnskii and Shirokov: let \(B\) be a Blaschke product with \(n\) zeros; then there exists an outer function \(\phi\), with \(\phi(0)=1\), such that \(||(B\phi)'||\leq Cn\), \(C\) being a constant independent of \(n\). Firstly, the authors give a simple proof of this result. Secondly, they apply this result to a certain problem of finding the asymptotics of orthogonal polynomials.
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orthogonal polynomials
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extremal problem
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Blaschke product
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CMV Matrix
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