Analytic completion of an open set
Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study the extension problem for functions defined on open subse...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/173.1 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/173.1 |
| Access Level: | acceso abierto |
| Palabra clave: | 517 Normed space Holomorphic function Bounding set Análisis matemático 1202 Análisis y Análisis Funcional |
| Sumario: | Let f be a holomorphic function on a complex normed space E. The possibility of extending f to the completion of E has been studied by Hirschowitz, Noverraz, Dineen, and Dineen-Noverraz. Here, following the ideas in [4, section 6.1], we study the extension problem for functions defined on open subsets of E. Moreover, through a complexification process, we use these results to obtain the analogous ones for analytic functions on real normed spaces. We note that in the real case we do not have, among other things, Cauchy inequalities and they are essential in the complex case. |
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