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Title: Functions Holomorphic along Holomorphic Vector Fields
Contributor(s): Kim, Kang-Tae (author); Poletsky, Evgeny (author); Schmalz, Gerd  (author)orcid 
Publication Date: 2009
DOI: 10.1007/s12220-009-9078-7
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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 φ 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.
Publication Type: Journal Article
Source of Publication: Journal of Geometric Analysis, 19(3), p. 655-666
Publisher: Springer New York LLC
Place of Publication: United States of America
ISSN: 1050-6926
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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