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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unbounded domains of normality


Authors: J. M. Anderson and A. Hinkkanen
Journal: Proc. Amer. Math. Soc. 126 (1998), 3243-3252
MSC (1991): Primary 30D05, 58F23
DOI: https://doi.org/10.1090/S0002-9939-98-04370-6
MathSciNet review: 1452790
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Abstract: Let $f$ be a transcendental entire function of order less than 1/2. We introduce the method of ``self-sustaining spread'' to study the components of the set of normality of such a function. We give a new proof of the fact that any preperiodic or periodic component of the set of normality of $f$ is bounded. We obtain the same conclusion for a wandering domain if the growth rate of $f$ is never too small.


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Additional Information

J. M. Anderson
Affiliation: Department of Mathematics, University College, London WC1E 6BT, United Kingdom

A. Hinkkanen
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

DOI: https://doi.org/10.1090/S0002-9939-98-04370-6
Received by editor(s): July 8, 1996
Received by editor(s) in revised form: March 10, 1997
Additional Notes: This research was completed while the first author was visiting the University of Illinois at Urbana-Champaign. He wishes to thank the Department of Mathematics for its kind hospitality.
The research of the second author was partially supported by the Alfred P. Sloan Foundation, by the U.S. National Science Foundation grant DMS 94-00999, and by the U.S. National Security Agency grant MDA904-95-H-1014.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1998 American Mathematical Society