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Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials.

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Title: Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials.
Authors: Bessonov, Roman1,2 (AUTHOR) bessonov@pdmi.ras.ru, Denisov, Sergey1,3,4 (AUTHOR) denissov@wisc.edu
Source: Journal of Functional Analysis. Jun2021, Vol. 280 Issue 12, pN.PAG-N.PAG. 1p.
Subjects: Schur functions, Generating functions, Entropy, Orthogonal polynomials, Polynomials, Oscillations
Abstract: Let μ be a measure from Szegő class on the unit circle T and let { f n } 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 f n on T for all n ⩾ 0. Then, we focus on an analog of Lusin's conjecture for polynomials { φ n } orthogonal with respect to measure μ and prove that pointwise convergence of { | φ n | } almost everywhere on T is equivalent to a certain condition on zeroes of φ n. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 149569450
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials.
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  Data: <searchLink fieldCode="AR" term="%22Bessonov%2C+Roman%22">Bessonov, Roman</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> bessonov@pdmi.ras.ru</i><br /><searchLink fieldCode="AR" term="%22Denisov%2C+Sergey%22">Denisov, Sergey</searchLink><relatesTo>1,3,4</relatesTo> (AUTHOR)<i> denissov@wisc.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Jun2021, Vol. 280 Issue 12, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Schur+functions%22">Schur functions</searchLink><br /><searchLink fieldCode="DE" term="%22Generating+functions%22">Generating functions</searchLink><br /><searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Let μ be a measure from Szegő class on the unit circle T and let { f n } 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 f n on T for all n ⩾ 0. Then, we focus on an analog of Lusin's conjecture for polynomials { φ n } orthogonal with respect to measure μ and prove that pointwise convergence of { | φ n | } almost everywhere on T is equivalent to a certain condition on zeroes of φ n. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jfa.2021.109002
    Languages:
      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Schur functions
        Type: general
      – SubjectFull: Generating functions
        Type: general
      – SubjectFull: Entropy
        Type: general
      – SubjectFull: Orthogonal polynomials
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Oscillations
        Type: general
    Titles:
      – TitleFull: Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials.
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            NameFull: Bessonov, Roman
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            NameFull: Denisov, Sergey
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            – D: 15
              M: 06
              Text: Jun2021
              Type: published
              Y: 2021
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              Value: 280
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              Value: 12
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            – TitleFull: Journal of Functional Analysis
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