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Topological duality on the function space H(C^N)


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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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
Uncontrolled Keywords:Holomorphic functions;
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16845

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Deposited On:24 Oct 2012 08:50
Last Modified:07 Feb 2014 09:36

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