Hypercyclic subspaces for sequences of finite order differential operators
It is proved that, if is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense -dimensional subspace of entire functions, all of who...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/172993 |
| Acceso en línea: | https://hdl.handle.net/11441/172993 https://doi.org/10.1016/j.jmaa.2025.129257 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential operator of finite orderHypercyclic sequence of operatorsMaximal dense lineabilitySpaceabilityPointwise lineability |
| Sumario: | It is proved that, if is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense -dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercyclic function. |
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