Martínez Ansemil, José María2023-06-212023-06-211979-01-01Martínez Ansemil, J. M. «Topological Duality on the Function Space H(CN)». Journal of Mathematical Analysis and Applications, vol. 67, n.o 1, enero de 1979, pp. 188-97. DOI.org (Crossref), https://doi.org/10.1016/0022-247X(79)90016-7.0022-247X10.1016/0022-247X(79)90016-7https://hdl.handle.net/20.500.14352/64682By 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.}engjournal articlehttps//doi.org/10.1016/0022-247X(79)90016-7http://www.journals.elsevier.com/http://www.sciencedirect.com/science/article/pii/0022247X79900167restricted access517.98Holomorphic functionsAnálisis funcional y teoría de operadores