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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A Schottky-type theorem for starlike domains in Banach spaces


Authors: Jorge Mujica and Paula Takatsuka
Journal: Proc. Amer. Math. Soc. 135 (2007), 1141-1144
MSC (2000): Primary 46G20, 46E50
Published electronically: October 11, 2006
MathSciNet review: 2262917
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if $ U$ is a starlike domain in a Banach space $ E$ and $ \mathscr{F}$ is a family of holomorphic functions on $ U$ that omit two distinct values and is bounded at the origin, then $ \mathscr{F}$ is uniformly bounded on each $ U$-bounded set.


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Additional Information

Jorge Mujica
Affiliation: IMECC - UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
Email: mujica@ime.unicamp.br

Paula Takatsuka
Affiliation: IMECC - UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
Email: ptakatsu@ime.unicamp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08681-3
PII: S 0002-9939(06)08681-3
Keywords: Banach space, balanced domain, starlike domain, holomorphic function, holomorphic function of bounded type.
Received by editor(s): November 11, 2005
Published electronically: October 11, 2006
Additional Notes: The second author was supported by a teaching assistantship from UNICAMP
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.