Normal Families and Omitted Functions

Let 𝓕 be a family of meromorphic functions on the plane domain D, all of whose zeros and poles are multiple. Let h be a meromorphic function which does not vanish on D. If for each f ∈ 𝓕, f′(z) ≠ h(z) for z ∈ D, then 𝓕 is normal on D.

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Bibliographic Details
Published in:	Indiana University mathematics journal Vol. 54; no. 1; pp. 223 - 235
Main Authors:	Pang, Xuecheng, Yang, Degui, Zalcman, Lawrence
Format:	Journal Article
Language:	English
Published:	Bloomington, IN Department of Mathematics of Indiana University 01-01-2005 Indiana University
Subjects:	Analytic functions Exact sciences and technology Functions of a complex variable Integers Mathematical analysis Mathematical functions Mathematical theorems Mathematics Meromorphic functions Multiplicity of function roots Polynomials Rational functions Sciences and techniques of general use Zero Mathematical analysis Meromorphic function
Online Access:	Get full text
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Summary:	Let 𝓕 be a family of meromorphic functions on the plane domain D, all of whose zeros and poles are multiple. Let h be a meromorphic function which does not vanish on D. If for each f ∈ 𝓕, f′(z) ≠ h(z) for z ∈ D, then 𝓕 is normal on D.
ISSN:	0022-2518 1943-5258
DOI:	10.1512/iumj.2005.54.2492