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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on the Bergman stability


Authors: Chen Boyong and Zhang Jinhao
Journal: Proc. Amer. Math. Soc. 128 (2000), 2903-2905
MSC (1991): Primary 32H10
Published electronically: February 29, 2000
MathSciNet review: 1664329
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Abstract:

Let $\{D_k\},k=1,2,\cdots$, be a sequence of bounded pseudoconvex domains that converges, in the sense of Boas, to a bounded domain $D$. We show that if $\partial D $ can be described locally as the graph of a continuous function in suitable coordinates for ${\mathbf C}^n$, then the Bergman kernel of $D_k$ converges to the Bergman kernel of $D$ uniformly on compact subsets of $D\times D$.


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Additional Information

Chen Boyong
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Address at time of publication: Department of Applied Mathematics, Tongji University,Shanghai 200092, People’s Republic of China

Zhang Jinhao
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05333-8
PII: S 0002-9939(00)05333-8
Keywords: Bergman kernel
Received by editor(s): July 20, 1998
Received by editor(s) in revised form: October 30, 1998
Published electronically: February 29, 2000
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society