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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bounded holomorphic functions of several complex variables. I


Author: Dong Sie Kim
Journal: Trans. Amer. Math. Soc. 158 (1971), 437-443
MSC: Primary 32.20
DOI: https://doi.org/10.1090/S0002-9947-1971-0280736-2
MathSciNet review: 0280736
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Abstract: A domain of bounded holomorphy in a complex analytic manifold is a maximal domain for which every bounded holomorphic function has a bounded analytic continuation. In this paper, we show that this is a local property: if, for each boundary point of a domain, there exists a bounded holomorphic function which cannot be continued to any neighborhood of the point, then there exists a single bounded holomorphic function which cannot be continued to any neighborhood of the boundary points.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0280736-2
Keywords: Ringed space, complex analytic manifold, quasi-analytic, hausdorff sheaf, analytic extension, analytic continuation, montel property, weak region of bounded holomorphy, region of bounded holomorphy, spectrum
Article copyright: © Copyright 1971 American Mathematical Society