Standard

Entropy function and orthogonal polynomials. / Bessonov, R. V.

в: Journal of Approximation Theory, Том 272, 105650, 12.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Bessonov, RV 2021, 'Entropy function and orthogonal polynomials', Journal of Approximation Theory, Том. 272, 105650. https://doi.org/10.1016/j.jat.2021.105650

APA

Bessonov, R. V. (2021). Entropy function and orthogonal polynomials. Journal of Approximation Theory, 272, [105650]. https://doi.org/10.1016/j.jat.2021.105650

Vancouver

Bessonov RV. Entropy function and orthogonal polynomials. Journal of Approximation Theory. 2021 Дек.;272. 105650. https://doi.org/10.1016/j.jat.2021.105650

Author

Bessonov, R. V. / Entropy function and orthogonal polynomials. в: Journal of Approximation Theory. 2021 ; Том 272.

BibTeX

@article{47732f6e5b8649fdaea9b840c710fa84,
title = "Entropy function and orthogonal polynomials",
abstract = "We give a simple proof of a classical theorem by A. M{\'a}t{\'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.",
keywords = "Christoffel–Darboux kernels, CMV basis, Freud theorem, M{\'a}t{\'e}–Nevai–Totik theorem, Scattering, Szeg{\H o} class, Universality limits",
author = "Bessonov, {R. V.}",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = dec,
doi = "10.1016/j.jat.2021.105650",
language = "English",
volume = "272",
journal = "Journal of Approximation Theory",
issn = "0021-9045",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Entropy function and orthogonal polynomials

AU - Bessonov, R. V.

N1 - Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/12

Y1 - 2021/12

N2 - We give a simple proof of a classical theorem by A. Máté, 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.

AB - We give a simple proof of a classical theorem by A. Máté, 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.

KW - Christoffel–Darboux kernels

KW - CMV basis

KW - Freud theorem

KW - Máté–Nevai–Totik theorem

KW - Scattering

KW - Szegő class

KW - Universality limits

UR - http://www.scopus.com/inward/record.url?scp=85115291511&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2021.105650

DO - 10.1016/j.jat.2021.105650

M3 - Article

AN - SCOPUS:85115291511

VL - 272

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

M1 - 105650

ER -

ID: 94392980