Normal families and uniqueness theorems for entire functions

Mingliang Fang; Lawrence Zalcman

doi:10.1016/S0022-247X(03)00041-6

Normal families and uniqueness theorems for entire functions

Mingliang Fang, Lawrence Zalcman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S, f) = E(S, f′), then f ≡ f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.

Original language	English
Pages (from-to)	273-283
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	280
Issue number	2
DOIs	https://doi.org/10.1016/S0022-247X(03)00041-6
State	Published - 15 Apr 2003

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: mlfang@pine.njnu.edu.cn (M. Fang), zalcman@macs.biu.ac.il (L. Zalcman). 1 Supported by the NNSF of China (Grant No. 10071038) and by the Fred and Barbara Kort Sino–Israel Post Doctoral Fellowship Program at Bar-Ilan University. 2 Research supported by the German–Israeli Foundation for Scientific Research and Development, GIF Grant No. G-643-117.6/1999.

Keywords

Derivative
Entire function
Normal family
Unicity

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10.1016/S0022-247X(03)00041-6

Cite this

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N2 - There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S, f) = E(S, f′), then f ≡ f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.

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KW - Normal family

KW - Unicity

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Normal families and uniqueness theorems for entire functions

Abstract

Bibliographical note

Keywords

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