Normal families of meromorphic functions with multiple zeros and poles期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Normal families of meromorphic functions with multiple zeros and poles

Authors:	Xuecheng?Pang author-information" > author-information__contact u-icon-before" > mailto:xcpang@euler.math.ecnu.edu.cn" title=" xcpang@euler.math.ecnu.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Lawrence?Zalcman

Affiliation:	(1) Department of Mathematics, East China Normal University, 200062 Shanghai, P.R. China;(2) Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Abstract:	LetF be a family of functions meromorphic in the plane domainD, all of whose zeros and poles are multiple. Leth be a continuous function onD. Suppose that, for eachf ≠F,f ¹(z) εh(z) forz εD. We show that ifh(z) ≠ 0 for allz εD, or ifh is holomorphic onD but not identically zero there and all zeros of functions inF have multiplicity at least 3, thenF is a normal family onD. Partially supported by the Shanghai Priority Academic Discipline and by the NNSF of China Approved No. 10271122. Research supported by the German-Israeli Foundation for Scientific Research and Development, G.I.F. Grant No. G-643-117.6/1999.

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