Normal families and omitted functions II

Guoming Zhang, Xuecheng Pang, Lawrence Zalcman

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Let k ≥ 2 be an integer and let ℱ be a family of functions meromorphic on a domain D in , all of whose poles are multiple and whose zeros all have multiplicity at least k + 1. Let h be a function meromorphic on D, h ≢ 0, ∞. Suppose that for each f ∈ ℱ, f(k)(z) ≠ h(z) for z ∈ D. Then ℱ is a normal family on D.

Original languageEnglish
Pages (from-to)63-71
Number of pages9
JournalBulletin of the London Mathematical Society
Volume41
Issue number1
DOIs
StatePublished - Feb 2009

Bibliographical note

Funding Information:
X. P. was supported by the NSSF of China Grant No. 10671067, and L. Z. was supported by the German–Israeli Foundation for Scientific Research and Development Grant G-809-234.6/2003 and Israel Science Foundation Grant 395/07.

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