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Sbornik: Mathematics, 2018, Volume 209, Issue 7, Pages 985–1018
DOI: https://doi.org/10.1070/SM8876 (Mi sm8876) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The growth of polynomials orthogonal on the unit circle with respect to a weight $w$ that satisfies $w,w^{-1}\in L^\infty(\mathbb{T})$

S. A. Denisovab

a Department of Mathematics, University of Wisconsin–Madison, Madison, WI, USA
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
English version PDF (679 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/SM8876
Abstract: We consider the polynomials $\{\varphi_n(z,w)\}$ orthogonal on the circle with respect to a weight $w$ that satisfies $w,w^{-1}\in L^\infty(\mathbb{T})$ and show that $\|\varphi_n(e^{i\theta},w)\|_{L^\infty(\mathbb{T})}$ can grow in $n$ at a certain rate.
Bibliography: 21 titles.
Keywords: polynomials orthogonal on the circle, Steklov's conjecture.
Funding agency Grant number
Russian Science Foundation 14-21-00025
National Science Foundation DMS1464479
The results in § \ref{s7} were obtained with the support of the Russian Science Foundation under grant no. 14-21-00025. The other results were obtained with the support of the National Science Foundation under grant no. DMS1464479.
Received: 07.12.2016 and 30.05.2017
Bibliographic databases:
Document Type: Article
UDC: 517.538.3
MSC: 42C05
Language: English
Original paper language: Russian
Citation: S. A. Denisov, “The growth of polynomials orthogonal on the unit circle with respect to a weight $w$ that satisfies $w,w^{-1}\in L^\infty(\mathbb{T})$”, Sb. Math., 209:7 (2018), 985–1018
Citation in format AMSBIB
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\by S.~A.~Denisov
\paper The growth of polynomials orthogonal on the unit circle with respect to a~weight~$w$ that satisfies $w,w^{-1}\in L^\infty(\mathbb{T})$
\jour Sb. Math.
\yr 2018
\vol 209
\issue 7
\pages 985--1018
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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