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|Title:||Functions Holomorphic along Holomorphic Vector Fields||Contributor(s):||Kim, Kang-Tae (author); Poletsky, Evgeny (author); Schmalz, Gerd (author)||Publication Date:||2009||DOI:||10.1007/s12220-009-9078-7||Handle Link:||https://hdl.handle.net/1959.11/3944||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||Statistics to Oct 2018:||Visitors: 134
|Appears in Collections:||Journal Article|
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