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Pré-Publication, Document De Travail Année : 2019

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

Résumé

The classical Szego polynomial approximation theorem states that the polynomials are dense in the space $L^2(\rho)$, where $\rho$ is a measure on the unit circle, if and only if the logarithmic integral of the measure $\rho$ 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 $\rho$ on a sufficiently rare subset of the circle.

Dates et versions

hal-02065962 , version 1 (13-03-2019)

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Alexander Borichev, Anna Kononova, Mikhail Sodin. Notes on the Szego minimum problem. I. Measures with deep zeroes. 2019. ⟨hal-02065962⟩
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