Exponential type of hypercyclic entire functions
In this paper the exponential type of hypercyclic entire functions with respect to a sequence (Φn(D)) of differential operators is considered, where every Φn is an entire function of exponential type. We prove that under suitable conditions certain rates of growth are possible for hypercyclicity whi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87483 |
| Acceso en línea: | https://hdl.handle.net/11441/87483 https://doi.org/0003-889X/02/040283-08 |
| Access Level: | acceso abierto |
| Palabra clave: | Entire function Hypercyclic function Infinite order differential operator Growth Exponential type Dense linear manifold |
| Sumario: | In this paper the exponential type of hypercyclic entire functions with respect to a sequence (Φn(D)) of differential operators is considered, where every Φn is an entire function of exponential type. We prove that under suitable conditions certain rates of growth are possible for hypercyclicity while others are not. In particular, our statements extend the negative part of a sharp result on growth of D-hypercyclic entire functions due to Grosse-Erdmann, and are related to a result by Chan and Shapiro about the existence of Φ(D)-hypercyclic functions in certain Hilbert spaces of entire functions. |
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