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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Integer translation of meromorphic functions


Authors: Jeong H. Kim and Lee A. Rubel
Journal: Trans. Amer. Math. Soc. 349 (1997), 1447-1462
MSC (1991): Primary 30D45
MathSciNet review: 1325918
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Abstract: Let $G$ be a given open set in the complex plane. We prove that there is an entire function such that its integer translations forms a normal family in a neighborhood of $z$ exactly for $z$ in $G$ if and only if $G$ is periodic with period 1, i.e., $z\pm 1\in G$ for all $z\in G$.


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Additional Information

Jeong H. Kim
Affiliation: Korea Military Academy, Seoul 139-799, Korea
Email: jkim@hwarang.kma.ac.kr

Lee A. Rubel
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01504-3
PII: S 0002-9947(97)01504-3
Received by editor(s): October 17, 1994
Received by editor(s) in revised form: March 31, 1995
Additional Notes: The research of the second author was partially supported by a grant from the National Science Foundation.
Article copyright: © Copyright 1997 American Mathematical Society