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Proceedings of the American Mathematical Society

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Extensions of holomorphic maps
through hypersurfaces and relations
to the Hartogs extensions in infinite dimension


Authors: Do Duc Thai and Nguyen Thai Son
Journal: Proc. Amer. Math. Soc. 128 (2000), 745-754
MSC (1991): Primary 32E05, 32H20; Secondary 32F05, 58B12
Published electronically: July 27, 1999
MathSciNet review: 1622985
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Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map $f$ from $Z$ $\setminus$ $H$ into $Y$, where $H$ is a hypersurface in a complex Banach manifold $Z$ and $Y$ is a hyperbolic Banach space. Under various assumptions on $Z$, $H$ and $Y$ we show that $f$ can be extended to a holomorphic map from $Z$ into $Y$. Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.


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Additional Information

Do Duc Thai
Affiliation: Department of Mathematics, Vietnam National University, Institute of Pedagogy, Cau Giay - Tu Liem, Hanoi, Vietnam
Email: ddthai@netnam.org.vn

Nguyen Thai Son
Affiliation: Department of Mathematics, Vietnam National University, Institute of Pedagogy, Cau Giay - Tu Liem, Hanoi, Vietnam

DOI: https://doi.org/10.1090/S0002-9939-99-05033-9
Received by editor(s): May 27, 1997
Received by editor(s) in revised form: April 20, 1998
Published electronically: July 27, 1999
Additional Notes: Supported by the State Program for Fundamental Research in Natural Science.
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society