Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials

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Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials. / Bessonov, Roman; Denisov, Sergey.

In: Journal of Functional Analysis, Vol. 280, No. 12, 109002, 15.06.2021.

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

Author

Bessonov, Roman ; Denisov, Sergey. / Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials. In: Journal of Functional Analysis. 2021 ; Vol. 280, No. 12.

BibTeX

@article{68b139e5407541db8b1943a7a38a1ae4,

title = "Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials",

abstract = "Let μ be a measure from Szeg{\H o} 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 Szeg{\H o}'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.",

keywords = "Bounded mean oscillation, Orthogonal polynomials, Szeg{\H o} class, Zero sets",

author = "Roman Bessonov and Sergey Denisov",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = jun,

day = "15",

doi = "10.1016/j.jfa.2021.109002",

language = "English",

volume = "280",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "12",

}

RIS

TY - JOUR

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

AU - Bessonov, Roman

AU - Denisov, Sergey

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 -

ID: 94393106