On the removable singularities of $L^2$ holomorphic functions

Abstract: Let $\Omega$ be a domain in $\mathbb{C}$ and $E$ a closed subset of $\Omega$. Carleson proved that if $E$ has zero logarithmic capacity, then any $L^2$ holomorphic function on $\Omega\setminus E$ can be holomorphically extended to $\Omega$. In particular, the Bergman kernel on $\Omega$ coincides with the Bergman kernel on $\Omega\setminus E$. In this talk, I will discuss the case where $E$ has small logarithmic capacity, and introduce an absolutely continuous property of the Bergman kernel, which also leads to a proof of Carleson's theorem.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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