Extension of entire functions on nuclear locally convex spaces
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- by Reinhold Meise and Dietmar Vogt
- Proc. Amer. Math. Soc. 92 (1984), 495-500
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760932-2
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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 $F$.References
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Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 495-500
- MSC: Primary 46G20; Secondary 46A12, 46E10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760932-2
- MathSciNet review: 760932