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Keywords:
weighted Bergman kernel; admissible weight; sequence of domains
weighted Bergman kernel; admissible weight; sequence of domains
Summary:
We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space $\mathbb C^N$, 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 M. Skwarczyński (1980), highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover, we show that convergence of weighted Bergman kernels implies this property, which will give a characterization of the domains, for which the inverse of the Ramadanov's theorem holds.
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