Universidad Complutense de Madrid
E-Prints Complutense

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

Impacto

Downloads

Downloads per month over past year

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

[img] PDF
Restringido a Repository staff only

451kB

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
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

Origin of downloads

Repository Staff Only: item control page