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Complex Approximations, Orthogonal Polynomials and Applications (CAOPA)
May 25, 2020 18:00, Moscow, online via Zoom
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Outside the Szegö condition: some proofs and disproofs
A. A. Kononova Saint Petersburg State University
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Abstract:
By the classical Szegö theorem the polynomials are dense in $L^2(\mu)$, where $\mu$ is a measure on the unit circle, if and only if the logarithmic integral of the density of $\mu$ diverges. We will discuss several quantitative versions of this theorem for the case of measure with a divergent logarithmic integral of its density. In particular, we will disprove one conjecture of Nevai. The talk is based on a joint work with A. Borichev and M. Sodin (arXiv:1902.00874, arXiv:1902.00872)
Language: English
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