TY - JOUR

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

AU - Borichev, Alexander

AU - Kononova, Anna

AU - Sodin, Mikhail

N1 - Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.

PY - 2020/10

Y1 - 2020/10

N2 - The classical Szegő 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 Szegő’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 Szegő 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 Szegő’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.

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

U2 - 10.1007/s11856-020-2077-x

DO - 10.1007/s11856-020-2077-x

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AN - SCOPUS:85094114710

SN - 0021-2172

VL - 240

SP - 725

EP - 743

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -