The spaces of analytic functions on open subsets of RN and CN
Loading...
Official URL
Full text at PDC
Publication date
2015
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
European Mathematical Society
Citations
Exportar
Citation
Martínez Ansemil, J. M., Ponte Miramontes, M. S. & López-Salazar Codes, J. «The Spaces of Analytic Functions on Open Subsets of $\mathbb R^{\mathbb N}$ and $\mathbb C^{\mathbb N}$». Publications of the Research Institute for Mathematical Sciences, vol. 51, n.o 1, abril de 2015, pp. 191-206. DOI.org (Crossref), https://doi.org/10.4171/prims/152.
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.