Normal families and uniqueness theorems for entire functions

Mingliang Fang, Lawrence Zalcman

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16 Scopus citations


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 languageEnglish
Pages (from-to)273-283
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Apr 2003

Bibliographical note

Funding Information:
* Corresponding author. E-mail addresses: (M. Fang), (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.


  • Derivative
  • Entire function
  • Normal family
  • Unicity


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