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Ansemil, José María M.
(1979)
*Topological duality on the function space H(C^N).*
Journal of Mathematical Analysis and Applications, 67
(1).
pp. 188-197.
ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/0022247X79900167

## Abstract

By a classical theorem, there is an isomorphism between the space of entire functions of exponential type on Cn,ExpCn, and the analytic functions on H(Cn),H′(Cn) [see, for example, F. Trèves, Topological vector spaces, distributions, and kernels, Academic Press, New York, 1967; MR0225131 (37 #726)]. In this note, the author extends this useful theorem to H(CN), the space of analytic functions on the countable product of complex lines. Specifically, he considers H(CN) endowed with the compact-open topology τ0 and the associated bornological topology τδ. For both τ=τ0 and τδ, the author characterizes the strong duals (H(CN),τ)′ as spaces of entire functions of exponential type on CN. {Reviewer's remark: In the meantime the author has shown (private communication) that these dual spaces are different.}

Item Type: | Article |
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Uncontrolled Keywords: | Holomorphic functions; |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16845 |

Deposited On: | 24 Oct 2012 08:50 |

Last Modified: | 09 Aug 2018 10:35 |

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