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Integer translation of meromorphic functions

Author(s): Jeong H. Kim; Lee A. Rubel
Journal: Trans. Amer. Math. Soc. 349 (1997), 1447-1462.
MSC (1991): Primary 30D45
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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 $z\in G$ .

References:

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7.: Paul Montel, Leçons sur les familles normals de fonctions analytiques et leurs applications, Paris, 1927.


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