Infinite dimensional holomorphic non-extendability and algebraic genericity
In this note, the linear structure of the family He(G) of holomorphic functions in a domain G of a complex Banach space that are not holomorphically continuable beyond the boundary of G is analyzed. More particularly, we prove that He(G) contains, except for zero, a closed (and a dense) vector space...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87516 |
| Acceso en línea: | https://hdl.handle.net/11441/87516 https://doi.org/10.1016/j.laa.2016.10.008 |
| Access Level: | acceso abierto |
| Palabra clave: | Lineability, maximal spaceability Maximal algebrability Non-continuable holomorphic functions Domain of existence Balanced domain |
| Sumario: | In this note, the linear structure of the family He(G) of holomorphic functions in a domain G of a complex Banach space that are not holomorphically continuable beyond the boundary of G is analyzed. More particularly, we prove that He(G) contains, except for zero, a closed (and a dense) vector space having maximal dimension, as well as a maximally generated free algebra. The results obtained complete a number of previous ones by several authors. |
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