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Normal families of holomorphic functions with multiple zeros

Author(s): Xuecheng Pang; Mingliang Fang; Lawrence Zalcman
Journal: Conform. Geom. Dyn. 11 (2007), 101-106.
MSC (2000): Primary 30D45
Posted: June 13, 2007
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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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Ming-liang Fang, A note on a problem of Hayman, Analysis 20 (2000), 45-49. MR 1757068 (2001a:30036)

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David Minda, Yosida functions, Lectures on Complex Analysis (Xian, 1987), (Chi Tai Chuang, ed.), World Scientific Pub. Co., Singapore, 1988, pp. 197-213. MR 996476 (90d:30097)

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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: 10.1090/S1088-4173-07-00162-2
PII: S 1088-4173(07)00162-2
Received by editor(s): February 28, 2007
Posted: 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.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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