Exceptional functions wandering on the sphere and normal families

Jürgen Grahl; Shahar Nevo

doi:10.1007/s11856-014-1054-7

Exceptional functions wandering on the sphere and normal families

Jürgen Grahl, Shahar Nevo

Department of Mathematics

University of Würzburg

Research output: Contribution to journal › Article › peer-review

9 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 language	English
Pages (from-to)	21-34
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	202
Issue number	1
DOIs	https://doi.org/10.1007/s11856-014-1054-7
State	Published - 2 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Hebrew University Magnes Press.

Funding

∗ Research of Shahar Nevo was supported by the Israel Science Foundation, Grant No. 395/07. 1 Schiff [12] calls it the “Fundamental Normality Test” (FNT). Received February 26, 2013 and in revised form May 8, 2013

Funders	Funder number
Israel Science Foundation	395/07

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10.1007/s11856-014-1054-7

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Exceptional functions wandering on the sphere and normal families

Abstract

Bibliographical note

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