Functions Holomorphic along Holomorphic Vector Fields
SCIE
SCOPUS
- Title
- Functions Holomorphic along Holomorphic Vector Fields
- Authors
- Kim, KT; Poletsky, E; Schmalz, G
- Date Issued
- 2009-07
- Publisher
- SPRINGER
- Abstract
- The main result of the paper is the following generalization of Forelli's theorem (Math. Scand. 41: 358-364, 1977): Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with eigenvalues whose ratios are positive reals. Then any function phi that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p. We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.
- Keywords
- Holomorphic functions; Holomorphic vector fields
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26204
- DOI
- 10.1007/S12220-009-9078-7
- ISSN
- 1050-6926
- Article Type
- Article
- Citation
- JOURNAL OF GEOMETRIC ANALYSIS, vol. 19, no. 3, page. 655 - 666, 2009-07
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