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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


Full text: PDF file (512 kB)
Full text: http:/.../preprint.asp?id=2016-40&lg=r
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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}


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