Holomorphic functions having large images under the action of differential operators
We prove in this note that, given a simply connected domain G in the complex plane and a sequence of infinite order linear differential operators generated by entire functions of subexponential type satisfying suitable conditions, then there are holomorphic functions f on G such that the image of an...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87506 |
| Acceso en línea: | https://hdl.handle.net/11441/87506 https://doi.org/10.1006/jmaa.1998.6201 |
| Access Level: | acceso abierto |
| Palabra clave: | Entire function of subexponential type Infinite order differential operator Residual set Holomorphic function Relatively compact sequence Linear metric space Large images |
| Sumario: | We prove in this note that, given a simply connected domain G in the complex plane and a sequence of infinite order linear differential operators generated by entire functions of subexponential type satisfying suitable conditions, then there are holomorphic functions f on G such that the image of any open subset under the action of those operators on f is arbitrarily large. This generalizes an earlier result about images of derivatives. A known statement about close orbits is also strengthened. |
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