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Normality Properties of the Family f(nz): n ∈ N

Normality Properties of the Family f(nz): n ∈ N A family Ƒ of meromorphic functions on a plane domain D is called quasi-normal on D if each sequence S of functions in Ƒ has a subsequence which converges locally χ-uniformly on D E, where E = E(S) is a subset of D having no accumulation points in D. The notion of quasi-normality was introduced by Montel. It generalizes the concept of normal family, which corresponds to E = ∅. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Normality Properties of the Family f(nz): n ∈ N

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Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03320997
Publisher site
See Article on Publisher Site

Abstract

A family Ƒ of meromorphic functions on a plane domain D is called quasi-normal on D if each sequence S of functions in Ƒ has a subsequence which converges locally χ-uniformly on D E, where E = E(S) is a subset of D having no accumulation points in D. The notion of quasi-normality was introduced by Montel. It generalizes the concept of normal family, which corresponds to E = ∅.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References