The spaces of analytic functions on open subsets of RN and CN
| dc.contributor.author | Martínez Ansemil, José María | |
| dc.contributor.author | Ponte Miramontes, María Del Socorro | |
| dc.contributor.author | López-Salazar Codes, Jerónimo | |
| dc.date.accessioned | 2023-06-19T14:54:07Z | |
| dc.date.available | 2023-06-19T14:54:07Z | |
| dc.date.issued | 2015 | |
| dc.description.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. | en |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30295 | |
| dc.identifier.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. | |
| dc.identifier.doi | 10.4171/PRIMS/152 | |
| dc.identifier.issn | 0034-5318 | |
| dc.identifier.officialurl | https//doi.org/10.4171/PRIMS/152 | |
| dc.identifier.relatedurl | https://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=51&iss=1&rank=5 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34661 | |
| dc.issue.number | 1 | |
| dc.journal.title | Publications of the Research Institute for Mathematical Sciences | |
| dc.page.final | 206 | |
| dc.page.initial | 191 | |
| dc.publisher | European Mathematical Society | |
| dc.rights.accessRights | metadata only access | |
| dc.subject.cdu | 51 | |
| dc.subject.keyword | Analytic function | |
| dc.subject.keyword | Locally convex topology | |
| dc.subject.keyword | Inductive limit | |
| dc.subject.ucm | Matemáticas (Matemáticas) | |
| dc.subject.unesco | 12 Matemáticas | |
| dc.title | The spaces of analytic functions on open subsets of RN and CN | en |
| dc.type | journal article | |
| dc.volume.number | 51 | |
| dspace.entity.type | Publication | |
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