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 Keldysh Institute preprints, 2016, 040, 19 pp. (Mi ipmp2116)

The Steklov problem and estimates for orthogonal polynomials with $A_p(\mathbb{T})$ weights

A. I. Aptekarev, S. A. Denisov

Abstract: The presented paper is devoted to bounds of the orthogonal polynomials on the support of the measure of orthogonality. The big interest to this subject-matter is caused by famous Steklov problem and it's modern development and understanding. We consider weights on the unit circle $\mathbb{T}$ with $A_p$ characteristic close to $1$. For the corresponding orthonormal polynomials, we obtain the upper estimates on the weighted $L^p$ norm with $p\in (2,\infty]$.

Keywords: orthogonal polynomials; Steklov problem; bounds of orthogonal polynomials on the circle; Muckenhoupt weights.

 Funding Agency Grant Number Russian Science Foundation 14-21-00025

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UDC: 517.53+517.9

Citation: A. I. Aptekarev, S. A. Denisov, “The Steklov problem and estimates for orthogonal polynomials with $A_p(\mathbb{T})$ weights”, Keldysh Institute preprints, 2016, 040, 19 pp.

Citation in format AMSBIB
\Bibitem{AptDen16} \by A.~I.~Aptekarev, S.~A.~Denisov \paper The Steklov problem and estimates for orthogonal polynomials with $A_p(\mathbb{T})$ weights \jour Keldysh Institute preprints \yr 2016 \papernumber 040 \totalpages 19 \mathnet{http://mi.mathnet.ru/ipmp2116}