The Bergman space of an open set D in the complex plane is the space of holomorphic square-integrable functions on D . As such, it is a basic object in complex analysis. It has been known for almost 40 years, that is either trivial or infinite dimensional. In this talk, I present some potential-theoretic conditions which further describe the dichotomy of the dimension of the Bergman space of D. Moreover, I explain how these results extend to bundle-valued Bergman spaces on compact Riemann surfaces. This talk is based on work with Purvi Gupta and Liz Vivas.
On bundle-valued Bergman space of compact Riemann surfaces
13.12.2022 14:00 - 15:00
Organiser:
Bernhard Lamel
Location: