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...

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Detalles Bibliográficos
Autores: Bernal González, Luis, Calderón Moreno, María del Carmen, Prado Bassas, José Antonio
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
Descripción
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.