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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

 

Normal families of holomorphic functions with multiple zeros


Authors: Xuecheng Pang, Mingliang Fang and Lawrence Zalcman
Journal: Conform. Geom. Dyn. 11 (2007), 101-106
MSC (2000): Primary 30D45
Published electronically: June 13, 2007
MathSciNet review: 2314245
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal F$ be a family of functions holomorphic on a domain $ D$ in $ \mathbb{C},$ all of whose zeros are multiple. Let $ h$ be a function meromorphic on $ D,$ $ h\not\equiv0,\infty.$ Suppose that for each $ f\in\mathcal F,$ $ f'(z)\ne h(z)$ for $ z\in D.$ Then $ \mathcal F$ is a normal family on $ D.$


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Additional Information

Xuecheng Pang
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Email: xcpang@euler.math.ecnu.edu.cn

Mingliang Fang
Affiliation: Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, People’s Republic of China
Email: hnmlfang@hotmail.com

Lawrence Zalcman
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: zalcman@macs.biu.ac.il

DOI: http://dx.doi.org/10.1090/S1088-4173-07-00162-2
PII: S 1088-4173(07)00162-2
Received by editor(s): February 28, 2007
Published electronically: June 13, 2007
Additional Notes: The first author’s research was supported by the NNSF of China (Grant No.\ 10671067).
The second author’s research was supported by the NNSF of China (Grant No.\ 10471065).
The third author’s research was supported by the German-Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.