On the growth of zero-free MacLane-universal entire functions
We show that exponential growth is the critical discrete rate of growth for zero-free entire functions which are universal in the sense of MacLane. Specifically, it is proved that if the lower exponential growth order of a zero-free entire function f is finite, then f cannot be hypercyclic for the d...
| 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:11441/87491 |
| Acceso en línea: | https://hdl.handle.net/11441/87491 https://doi.org/10.1016/j.indag.2011.12.003 |
| Access Level: | acceso abierto |
| Palabra clave: | Universal functions D-hypercyclicity Zerofree functions Exponential growth of entire functions Final set |
| Sumario: | We show that exponential growth is the critical discrete rate of growth for zero-free entire functions which are universal in the sense of MacLane. Specifically, it is proved that if the lower exponential growth order of a zero-free entire function f is finite, then f cannot be hypercyclic for the derivative operator; and, if a positive function ϕ having infinite exponential growth is fixed, then there exist zero-free hypercyclic functions which are controlled by ϕ along a sequence of radii tending to infinity. |
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