Exceptional functions/values wandering on the sphere and normal families

Seminar
Speaker
Dr. Shahar Nevo, Bar-Ilan University
Date
11/11/2013 - 14:00Add to Calendar 2013-11-11 14:00:00 2013-11-11 14:00:00 Exceptional functions/values wandering on the sphere and normal families We extend Caratheodory'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. We also introduce a somewhat "strange" result about some sharing wandering values assumptions that imply normality. אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

We extend Caratheodory'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. We also introduce a somewhat "strange" result about some
sharing wandering values assumptions that imply normality.

Last Updated Date : 04/11/2013