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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Holomorphic functions on nuclear spaces


Author: Philip J. Boland
Journal: Trans. Amer. Math. Soc. 209 (1975), 275-281
MSC: Primary 46G05; Secondary 46A30
DOI: https://doi.org/10.1090/S0002-9947-1975-0388094-3
MathSciNet review: 0388094
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Abstract: The space $ \mathcal{H}(E)$ of holomorphic functions on a quasi-complete nuclear space is investigated. If $ \mathcal{H}(E)$ is endowed with the compact open topology, it is shown that $ \mathcal{H}(E)$ is nuclear if and only if $ E'$ (continuous dual of $ E$) is nuclear. If $ E$ is a $ \mathcal{D}FN$ (dual of a Fréchet nuclear space) and $ F$ is a closed subspace of $ E$, then the restriction mapping $ \mathcal{H}(E) \to \mathcal{H}(F)$ is a surjective strict morphism.


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  • [1] Jorge Alberto Barroso, Mário C. Matos, and Leopoldo Nachbin, On bounded sets of holomorphic mappings, Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973) Springer, Berlin, 1974, pp. 123–134. Lecture Notes in Math., Vol. 364. MR 0394200
  • [2] Philip J. Boland, Malgrange theorem for entire functions on nuclear spaces, Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973) Springer, Berlin, 1974, pp. 135–144. Lecture Notes in Math., Vol. 364. MR 0420271
  • [3] Seán Dineen, Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on \cal𝐻(𝑈), Ann. Inst. Fourier (Grenoble) 23 (1973), no. 1, 19–54 (English, with French summary). MR 0500153
  • [4] John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
  • [5] Leopoldo Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, Springer-Verlag New York Inc., New York, 1969. MR 0254579
  • [6] Albrecht Pietsch, Nuclear locally convex spaces, Springer-Verlag, New York-Heidelberg, 1972. Translated from the second German edition by William H. Ruckle; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66. MR 0350360

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DOI: https://doi.org/10.1090/S0002-9947-1975-0388094-3
Article copyright: © Copyright 1975 American Mathematical Society