TY - JOUR

T1 - Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials

AU - Bessonov, Roman

AU - Denisov, Sergey

N1 - Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/6/15

Y1 - 2021/6/15

N2 - Let μ be a measure from Szegő class on the unit circle T and let {fn} be the family of Schur functions generated by μ. In this paper, we prove a version of the classical Szegő's formula, which controls the oscillation of fn on T for all n⩾0. Then, we focus on an analog of Lusin's conjecture for polynomials {φn} orthogonal with respect to measure μ and prove that pointwise convergence of {|φn|} almost everywhere on T is equivalent to a certain condition on zeroes of φn.

AB - Let μ be a measure from Szegő class on the unit circle T and let {fn} be the family of Schur functions generated by μ. In this paper, we prove a version of the classical Szegő's formula, which controls the oscillation of fn on T for all n⩾0. Then, we focus on an analog of Lusin's conjecture for polynomials {φn} orthogonal with respect to measure μ and prove that pointwise convergence of {|φn|} almost everywhere on T is equivalent to a certain condition on zeroes of φn.

KW - Bounded mean oscillation

KW - Orthogonal polynomials

KW - Szegő class

KW - Zero sets

UR - http://www.scopus.com/inward/record.url?scp=85102900888&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2021.109002

DO - 10.1016/j.jfa.2021.109002

M3 - Article

AN - SCOPUS:85102900888

VL - 280

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 12

M1 - 109002

ER -