Resumen:
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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 ?0 and the associated bornological topology ??. For both ?=?0 and ??, the author characterizes the strong duals (H(CN),?)? 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.}
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