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The spaces of analytic functions on open subsets of RN and CN

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Ansemil, José María M. and Ponte, Socorro and López-Salazar Codes, Jerónimo (2015) The spaces of analytic functions on open subsets of RN and CN. Publications of the Research Institute for Mathematical Sciences, 51 (1). pp. 191-206. ISSN 0034-5318

Official URL: https://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=1&rank=5


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Abstract

This paper is devoted to studying the space A(U) of all analytic functions on an open subset U of ℝℕ or ℂℕ. It is proved that if U satisfies a weak condition (that will be called the 0-property), then every f ϵ A(U) depends only on afinite number of variables. Several topologies on A(U) are then studied: the compact-open topology, the Tδ topology (already known in spaces of holomorphic functions) and a new one, defined by the inductive limit of the subspaces of analytic functions which only depend on a finite number of variables.


Item Type:Article
Uncontrolled Keywords:analytic function, locally convex topology, inductive limit
Subjects:Sciences > Mathematics
ID Code:30295
Deposited On:22 May 2015 08:42
Last Modified:22 May 2015 08:42

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