Weighted generalization of the Ramadanov's theorem and further considerations

Zbigniew Pasternak-Winiarski; Paweł Wójcicki

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 3, page 829-842
  • ISSN: 0011-4642

Abstract

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We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space 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.

How to cite

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Pasternak-Winiarski, Zbigniew, and Wójcicki, Paweł. "Weighted generalization of the Ramadanov's theorem and further considerations." Czechoslovak Mathematical Journal 68.3 (2018): 829-842. <http://eudml.org/doc/294802>.

@article{Pasternak2018,
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.},
author = {Pasternak-Winiarski, Zbigniew, Wójcicki, Paweł},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted Bergman kernel; admissible weight; sequence of domains},
language = {eng},
number = {3},
pages = {829-842},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weighted generalization of the Ramadanov's theorem and further considerations},
url = {http://eudml.org/doc/294802},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Pasternak-Winiarski, Zbigniew
AU - Wójcicki, Paweł
TI - Weighted generalization of the Ramadanov's theorem and further considerations
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 3
SP - 829
EP - 842
AB - 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.
LA - eng
KW - weighted Bergman kernel; admissible weight; sequence of domains
UR - http://eudml.org/doc/294802
ER -

References

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