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Transactions of the American Mathematical Society

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The Bergman kernel function and proper holomorphic mappings


Author: Steven R. Bell
Journal: Trans. Amer. Math. Soc. 270 (1982), 685-691
MSC: Primary 32H10; Secondary 32F15
DOI: https://doi.org/10.1090/S0002-9947-1982-0645338-1
MathSciNet review: 645338
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Abstract: It is proved that a proper holomorphic mapping $ f$ between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, $ {f^{ - 1}}(0) = \{ 0\} $, then $ f$ is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0645338-1
Article copyright: © Copyright 1982 American Mathematical Society

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