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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Keywords: Entire functions of uniformly bounded type, extension of entire functions, nuclear locally convex spaces
Article copyright: © Copyright 1984 American Mathematical Society