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

 

Extension of entire functions on nuclear locally convex spaces


Authors: Reinhold Meise and Dietmar Vogt
Journal: Proc. Amer. Math. Soc. 92 (1984), 495-500
MSC: Primary 46G20; Secondary 46A12, 46E10
MathSciNet review: 760932
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Abstract: We prove that for a nuclear locally convex complex vector space every entire function is the pull-back of some entire function on an appropriate Banach space if and only if the entire functions on $ E$ have the following universal extension property: whenever $ E$ is a topological linear subspace of a locally convex space $ F$ with a fundamental system of seminorms induced by semi-inner products, then every entire function $ f$ on $ E$ can be extended to an entire function on $ F$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760932-2
PII: S 0002-9939(1984)0760932-2
Keywords: Entire functions of uniformly bounded type, extension of entire functions, nuclear locally convex spaces
Article copyright: © Copyright 1984 American Mathematical Society