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

Martínez Ansemil, José M. and López Salazar, Jerónimo and Ponte Miramontes, Socorro (2015). The spaces of analytic functions on open subsets of RN and CN. "Publications of the Research Institute For Mathematical Sciences", v. 51 (n. 1); pp. 191-206. ISSN 0034-5318. https://doi.org/10.4171/PRIMS/152.

Description

Title: The spaces of analytic functions on open subsets of RN and CN
Author/s:
  • Martínez Ansemil, José M.
  • López Salazar, Jerónimo
  • Ponte Miramontes, Socorro
Item Type: Article
Título de Revista/Publicación: Publications of the Research Institute For Mathematical Sciences
Date: 2015
ISSN: 0034-5318
Volume: 51
Subjects:
Freetext Keywords: analytic function, locally convex topology, inductive limit
Faculty: E.T.S.I. y Sistemas de Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper is devoted to study 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 0-property), then every f∈A(U) depends only on a finite number of variables. Then several topologies on A(U) are studied: the compact open topology, the τδ 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 the first variables.

More information

Item ID: 44793
DC Identifier: http://oa.upm.es/44793/
OAI Identifier: oai:oa.upm.es:44793
DOI: 10.4171/PRIMS/152
Official URL: http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=1&rank=5
Deposited by: Memoria Investigacion
Deposited on: 28 Mar 2017 13:32
Last Modified: 28 Mar 2017 13:32
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