Czechoslovak Mathematical Journal, Vol. 68, No. 3, pp. 829-842, 2018
Weighted generalization of the Ramadanov's theorem and further considerations
Zbigniew Pasternak-Winiarski, Paweł Wójcicki
Received January 7, 2017. Published online May 9, 2018.
Abstract: 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.
Keywords: weighted Bergman kernel; admissible weight; sequence of domains
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Affiliations: Zbigniew Pasternak-Winiarski, Paweł M. Wójcicki, Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland, e-mail: z.pasternak-winiarski@mini.pw.edu.pl, p.wojcicki@mini.pw.edu.pl
