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

 

Some generalizations of Chirka's extension theorem


Author: Gautam Bharali
Journal: Proc. Amer. Math. Soc. 129 (2001), 3665-3669
MSC (2000): Primary 32D15
Published electronically: April 26, 2001
MathSciNet review: 1860501
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Abstract:

In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of $S \cup (\partial D \times D)$ - where $D$ is the open unit disc in $\mathbb{C} $ and $S$ is the graph of a continuous $D-$valued function on $\overline{D}$ - to higher dimensions, for certain classes of graphs $S \subseteq \overline{D} \times {D}^{n}, n>1$. In particular, we show that Chirka's extension theorem generalizes to configurations in ${\mathbb{C} }^{n+1}, n>1$, involving graphs of (non-holomorphic) polynomial maps with small coefficients.


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Additional Information

Gautam Bharali
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: bharali@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06020-8
PII: S 0002-9939(01)06020-8
Keywords: Holomorphic extension
Received by editor(s): May 1, 2000
Published electronically: April 26, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society



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