Entropy function and orthogonal polynomials

Standard

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

In: Journal of Approximation Theory, Vol. 272, 105650, 12.2021.

Research output: Contribution to journal › Article › peer-review

Author

Bessonov, R. V. / Entropy function and orthogonal polynomials. In: Journal of Approximation Theory. 2021 ; Vol. 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.

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