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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. E.M. Chirka, Generalized Hartogs' lemma and non-linear $\overline{\partial }-$equation, Complex analysis in contemporary mathematics (E.M. Chirka, ed.), Fasis, Moscow (in Russian) (to appear).
  • 2. Evgeni Chirka and Jean-Pierre Rosay, Remarks on the proof of a generalized Hartogs lemma, Ann. Polon. Math. 70 (1998), 43–47. Complex analysis and applications (Warsaw, 1997). MR 1668715
  • 3. Jean Pierre Rosay, A counterexample related to Hartogs’ phenomenon (a question by E. Chirka), Michigan Math. J. 45 (1998), no. 3, 529–535. MR 1653267, 10.1307/mmj/1030132298

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32D15

Retrieve articles in all journals with MSC (2000): 32D15


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
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