An extension of one direction in Marty's normality criterion

Jürgen Grahl; Shahar Nevo

doi:https://doi.org/10.1007/s00605-013-0561-7

An extension of one direction in Marty's normality criterion

Jürgen Grahl, Shahar Nevo

Department of Mathematics

Bar-Ilan University

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

Abstract

We prove the following extension of one direction in Marty's theorem: If k is a natural number, α > 1 and F is a family of functions meromorphic on a domain D all of whose poles have multiplicity at least k/α-1, then the normality of F implies that the family (Formula presented.) is locally uniformly bounded.

Original language	English
Pages (from-to)	205-217
Number of pages	13
Journal	Monatshefte fur Mathematik
Volume	174
Issue number	2
DOIs	https://doi.org/10.1007/s00605-013-0561-7
State	Published - Jun 2014

Keywords

Marty's theorem
Nevanlinna theory
Normal families

All Science Journal Classification (ASJC) codes

General Mathematics

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https://doi.org/10.1007/s00605-013-0561-7

Cite this

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title = "An extension of one direction in Marty's normality criterion",

abstract = "We prove the following extension of one direction in Marty's theorem: If k is a natural number, α > 1 and F is a family of functions meromorphic on a domain D all of whose poles have multiplicity at least k/α-1, then the normality of F implies that the family (Formula presented.) is locally uniformly bounded.",

keywords = "Marty's theorem, Nevanlinna theory, Normal families",

author = "J{\"u}rgen Grahl and Shahar Nevo",

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AB - We prove the following extension of one direction in Marty's theorem: If k is a natural number, α > 1 and F is a family of functions meromorphic on a domain D all of whose poles have multiplicity at least k/α-1, then the normality of F implies that the family (Formula presented.) is locally uniformly bounded.

KW - Marty's theorem

KW - Nevanlinna theory

KW - Normal families

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ER -

An extension of one direction in Marty's normality criterion

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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