Some generalizations of Chirka’s extension theorem
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- by Gautam Bharali PDF
- Proc. Amer. Math. Soc. 129 (2001), 3665-3669 Request permission
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
- 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).
- 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, DOI 10.4064/ap-70-1-43-47
- 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, DOI 10.1307/mmj/1030132298
Additional Information
- Gautam Bharali
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
- Email: bharali@math.wisc.edu
- Received by editor(s): May 1, 2000
- Published electronically: April 26, 2001
- Communicated by: Steven R. Bell
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3665-3669
- MSC (2000): Primary 32D15
- DOI: https://doi.org/10.1090/S0002-9939-01-06020-8
- MathSciNet review: 1860501