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International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
October 11, 2016 11:00–11:50, Moscow, Steklov Mathematical Institute, Conference hall, 9th floor

Strong asymptotics for Bergman and Szegő polynomials for non-smooth domains and curves

N. Stylianopoulos

University of Cyprus
 Video records: MP4 432.1 Mb MP4 1,703.1 Mb Materials: Adobe PDF 281.3 Kb

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Abstract: Strong asymptotics for Bergman polynomials (i.e., polynomials orthonormal with respect to the area measure on a bounded domain $G$ in $\mathbb{C}$) and Szegő polynomials (i.e., polynomials orthonormal with respect to the arclength measure on a rectifiable Jordan curve $\Gamma$ in $\mathbb{C}$) have been first derived in the early 1920's by T. Carleman, for Bergman polynomials, and by G. Szegő, for the namesake polynomials, in cases when $\partial G$ and $\Gamma$ are analytic Jordan curves.
The transition from analytic to smooth was not obvious and it took almost half a century, in the 1960's, till P. K. Suetin has been able to derive similar asymptotics for both kind of polynomials, in cases when $\partial G$ and $\Gamma$ are smooth Jordan curves.
The purpose on the talk is to report on some recent results on the strong asymptotics of Bergman and Szegő polynomials, in cases when $\partial G$ and $\Gamma$ are non-smooth Jordan curves, in particular, piecewise analytic without cusps.

Materials: presentation.pdf (281.3 Kb)

Language: English

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