Rigidity theorem of the Bergman kernel and the analytic capacity

Abstract: The Bergman kernel function of a domain D in the complex plane is the reproducing integral kernel for the Hilbert space of square integrable holomorphic functions on D. It is easily shown that the (on-diagonal) Bergman kernel is bounded below by the reciprocal of the volume of the domain D. In this talk, I geometrically characterize the domains whose Bergman kernels achieve the lower bound.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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