Entropy function and orthogonal polynomials
Complex Variables
2022-02-28 v1
Abstract
We give a simple proof of a classical theorem by A.M\'at\'e, P.Nevai, and V.Totik on asymptotic behavior of orthogonal polynomials on the unit circle. It is based on a new real-variable approach involving an entropy estimate for the orthogonality measure. Our second result is an extension of a theorem by G.Freud on averaged convergence of Fourier series. We also discuss some related open problems in the theory of orthogonal polynomials on the unit circle.
Cite
@article{arxiv.2104.11196,
title = {Entropy function and orthogonal polynomials},
author = {R. V. Bessonov},
journal= {arXiv preprint arXiv:2104.11196},
year = {2022}
}
Comments
14 pages, 2 open problems