Zbigniew Pasternak-Winiarski

Ramadanov theorem for weighted Bergman kernels

We study the limit behavior of weighted Bergman kernels on a sequence of domains in complex space $\CC^N$, and show that under some conditions on domains and weights, weighed Bergman kernels converge uniformly on compact sets. Then we give a weighted generalization of the theorem given by
Skwarczy\'nski, highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover we will show that convergence of weighted Bergman kernels implies this property.