Notes on the Szego minimum problem. I. Measures with deep zeroes

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Notes on the Szego minimum problem. I. Measures with deep zeroes. / Borichev, Alexander; Kononova, Anna ; Sodin, Mikhail.

In: Israel Journal of Mathematics, Vol. 240, No. 2, 10.2020, p. 725-743.

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

Author

Borichev, Alexander ; Kononova, Anna ; Sodin, Mikhail. / Notes on the Szego minimum problem. I. Measures with deep zeroes. In: Israel Journal of Mathematics. 2020 ; Vol. 240, No. 2. pp. 725-743.

BibTeX

@article{52f305628a894c6f95b8a15788dd1574,

title = "Notes on the Szego minimum problem. I. Measures with deep zeroes",

abstract = "The classical Szego polynomial approximation theorem states that the polynomials are dense in the space L2(ρ), where ρ is a measure on the unit circle, if and only if the logarithmic integral of the measure ρ diverges. In this note we give a quantitative version of Szego's theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure ρ on a sufficiently rare subset of the circle.",

keywords = "POLYNOMIALS",

author = "Alexander Borichev and Anna Kononova and Mikhail Sodin",

note = "Funding Information: Supported by a joint grant of Russian Foundation for Basic Research and CNRS (projects 17-51-150005-NCNI-a and PRC CNRS/RFBR 2017-2019) and by the project ANR-18-CE40-0035. Funding Information: Supported by a joint grant of Russian Foundation for Basic Research and CNRS (projects 17-51-150005-NCNI-a and PRC CNRS/RFBR 2017–2019). Funding Information: Supported by ERC Advanced Grant 692616 and ISF Grant 382/15.",

year = "2020",

month = oct,

doi = "10.1007/s11856-020-2077-x",

language = "English",

volume = "240",

pages = "725--743",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Notes on the Szego minimum problem. I. Measures with deep zeroes

AU - Borichev, Alexander

AU - Kononova, Anna

AU - Sodin, Mikhail

N1 - Funding Information: Supported by a joint grant of Russian Foundation for Basic Research and CNRS (projects 17-51-150005-NCNI-a and PRC CNRS/RFBR 2017-2019) and by the project ANR-18-CE40-0035. Funding Information: Supported by a joint grant of Russian Foundation for Basic Research and CNRS (projects 17-51-150005-NCNI-a and PRC CNRS/RFBR 2017–2019). Funding Information: Supported by ERC Advanced Grant 692616 and ISF Grant 382/15.

PY - 2020/10

Y1 - 2020/10

N2 - The classical Szego polynomial approximation theorem states that the polynomials are dense in the space L2(ρ), where ρ is a measure on the unit circle, if and only if the logarithmic integral of the measure ρ diverges. In this note we give a quantitative version of Szego's theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure ρ on a sufficiently rare subset of the circle.

AB - The classical Szego polynomial approximation theorem states that the polynomials are dense in the space L2(ρ), where ρ is a measure on the unit circle, if and only if the logarithmic integral of the measure ρ diverges. In this note we give a quantitative version of Szego's theorem in the special case when the divergence of the logarithmic integral is caused by deep zeroes of the measure ρ on a sufficiently rare subset of the circle.

KW - POLYNOMIALS

UR - https://arxiv.org/abs/1902.00874

UR - http://www.scopus.com/inward/record.url?scp=85094114710&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2889651f-2f0a-3032-9562-81a3841917d1/

U2 - 10.1007/s11856-020-2077-x

DO - 10.1007/s11856-020-2077-x

M3 - Article

VL - 240

SP - 725

EP - 743

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -

ID: 50663480