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arXiv · 0811.1093

Functions holomorphic along holomorphic vector fields

Kang-Tae Kim·Evgeny Poletsky·Gerd Schmalz
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Abstract

The main result of the paper is the following generalization of Forelli's theorem: 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 the 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.

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Kang-Tae Kim, Evgeny Poletsky, Gerd Schmalz. 2008-11-07. Functions holomorphic along holomorphic vector fields. https://doi.org/10.1007/s12220-009-9078-7

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