The Bergman kernel for circular multiply connected domains

摘要

The Bergman kernel is written in terms of a Poincare series for every circular multiply connected domain in the plane. The proposed exact formula is based on the Green's function constructed by Mityushev and S. V. Rogosin for multiply connected domains. First we verify the relation between the Green's function and the Bergman kernel for unbounded domains. Then we apply it to construct the Bergman kernel.