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

Alexander Borichev, Anna Kononova, Mikhail Sodin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)725-743
Number of pages19
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Oct 2020


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