Linear Kierst-Szpilrajn theorems
We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87529 |
| Acceso en línea: | https://hdl.handle.net/11441/87529 https://doi.org/10.4064/sm166-1-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Domain of holomorphy Unit disk Residual set Dense linear manifold Closed linear manifold Ggap series |
| Sumario: | We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in D whose domain of holomorphy is D except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic functions. |
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