Kim, Kang-Tae; Poletsky, Evgeny; Schmalz, Gerd

Author(s)

Kim, Kang-Tae

Poletsky, Evgeny

Schmalz, Gerd

Publication Date

2009

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.

Citation

Journal of Geometric Analysis, 19(3), p. 655-666

ISSN

1559-002X

1050-6926

Link

https://hdl.handle.net/1959.11/3944

Publisher

Springer New York LLC

Title

Functions Holomorphic along Holomorphic Vector Fields

Type of document

Journal Article

Entity Type

Publication

Author(s)	Kim, Kang-Tae Poletsky, Evgeny Schmalz, Gerd
Publication Date	2009
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.
Citation	Journal of Geometric Analysis, 19(3), p. 655-666
ISSN	1559-002X 1050-6926
Link	https://hdl.handle.net/1959.11/3944
Publisher	Springer New York LLC
Title	Functions Holomorphic along Holomorphic Vector Fields
Type of document	Journal Article
Entity Type	Publication

Functions Holomorphic along Holomorphic Vector Fields

Files: