Large subspaces of compositionally universal functions with maximal cluster sets
Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (φn), we construct an H(G)-dense linear manifold –as well as a closed infinite-dimensional linear manifold– all of whose non-zero functions have H(G)-dense orbits under the acti...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/45729 |
| Acceso en línea: | http://hdl.handle.net/11441/45729 https://doi.org/10.1016/j.jat.2011.10.005 |
| Access Level: | acceso abierto |
| Palabra clave: | Universal functions Hypercyclic vectors Composition operators Maximal cluster set Dense-lineability Spaceability |
| Sumario: | Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (φn), we construct an H(G)-dense linear manifold –as well as a closed infinite-dimensional linear manifold– all of whose non-zero functions have H(G)-dense orbits under the action of the sequence of composition operators associated to (φn). Simultaneously, these functions also present maximal cluster sets along each member of a large class of curves in G tending to the boundary. |
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