The Bergman Kernel and the ∂-Neumann Problem

Dr. Siqi Fu

Mathematics Department
Texas A&M University

March 9, 1998

Abstract

The Bergman kernel functions are the reproducing kernels for the space of square integrable holomorphic functions on domains in complex variables. The study of these kernel functions has repercussions in other areas of mathematics such as complex geometry, operator theory, and partial differential equations. These kernel functions are almost never explicitly computable. In the first part of my talk, however, I shall show how to compute the Bergman kernel functions of some special domains in a simple but systematic way. When explicit formulas are not available, properties of the Bergman kernel functions can be obtained by studying the ∂-Neumann problem. This problem is the topic of the second part of my talk.