ABSTRACT
The reader should suspect that, because boundary integrals can readily be turned into solid integrals by means of the Green’s formula, the Bergman kernel and the Szego˝ kernel of a domain should be closely related. In this chapter, we show that they are very closely related indeed.
Theorem 25.1. If Ω is a bounded simply connected domain with C∞
smooth boundary, then the Bergman kernel K(z, a) associated to Ω is related to the Szego˝ kernel via the identity
