Normal families of holomorphic functions with multiple zeros

Pang, Xuecheng; Fang, Mingliang; Zalcman, Lawrence

doi:10.1090/S1088-4173-07-00162-2

Normal families of holomorphic functions with multiple zeros
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by Xuecheng Pang, Mingliang Fang and Lawrence Zalcman

Conform. Geom. Dyn. 11 (2007), 101-106

DOI: https://doi.org/10.1090/S1088-4173-07-00162-2

Published electronically: 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 $D,$ $h\not \equiv 0,\infty .$ 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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