RT Journal Article
T1 The spaces of analytic functions on open subsets of RN and CN
A1 Martínez Ansemil, José María
A1 Ponte Miramontes, María Del Socorro
A1 López-Salazar Codes, Jerónimo
AB 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.
PB European Mathematical Society
SN 0034-5318
YR 2015
FD 2015
LK https://hdl.handle.net/20.500.14352/34661
UL https://hdl.handle.net/20.500.14352/34661
NO 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.
DS Docta Complutense
RD 8 abr 2025