Normal families and uniqueness theorems for entire functions

Mingliang Fang, Lawrence Zalcman

Research output: Contribution to journalArticlepeer-review

16 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 languageEnglish
Pages (from-to)273-283
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume280
Issue number2
DOIs
StatePublished - 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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