Exceptional functions wandering on the sphere and normal families

Jürgen Grahl, Shahar Nevo

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We extend Carathéodory’s generalization of Montel’s fundamental normality test to “wandering” exceptional functions (i.e., depending on the respective function in the family under consideration), and we give a corresponding result on shared functions. Furthermore, we prove that if we have a family of pairs (a, b) of functions meromorphic in a domain such that a and b uniformly “stay away from each other,” then the families of the functions a resp. b are normal. The proofs are based on a “simultaneous rescaling” version of Zalcman’s lemma.

Original languageEnglish
Pages (from-to)21-34
Number of pages14
JournalIsrael Journal of Mathematics
Volume202
Issue number1
DOIs
StatePublished - 2 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Hebrew University Magnes Press.

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