Geodesic
Weighted generalization of the Ramadanov's theorem and further considerations
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 829-842

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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.
DOI : 10.21136/CMJ.2018.0010-17
Classification : 32A25, 32A36
Keywords: weighted Bergman kernel; admissible weight; sequence of domains 
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     title = {Weighted generalization of the {Ramadanov's} theorem and further considerations},
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Pasternak-Winiarski, Zbigniew; Wójcicki, Paweł. Weighted generalization of the Ramadanov's theorem and further considerations. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 3, pp. 829-842. doi: 10.21136/CMJ.2018.0010-17

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