Weighted generalization of the Ramadanov theorem and further considerations

2016/12/16 by Zbigniew Pasternak-Winiarski, Pasternak-Winiarski, Zbigniew, Paweł M. Wójcicki +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1612.05619

openalex publication_date 2016/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 in [S, p. 38], 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, which will give a characterization of the domains, for which the inverse of Ramadanov theorem holds.

Related

• Reproducing kernels of some weighted Bergman spaces
• Weighted Kernel Functions on Planar Domains
• Invariant weighted Bergman metrics on domains
• Toeplitz operators and weighted Bergman kernels
• Pointwise estimates of weighted Bergman kernels in several complex variables