Hypercyclic sequences of differential and antidifferential operators
In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space of entire functions of several complex variables. Specifically, we generalize in several directions a theorem about hypercyclicity of certain infinite order linear differential op...
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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:11441/87536 |
| Acceso en línea: | https://hdl.handle.net/11441/87536 https://doi.org/10.1006/jath.1998.3237 |
| Access Level: | acceso abierto |
| Palabra clave: | Hypercyclic operator Hypercyclic sequence Fréchet space Invariant linear manifold Analytic function of several complex variables Runge domain Infinite order differential and antidifferential operators Zero-free function |
| Sumario: | In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space of entire functions of several complex variables. Specifically, we generalize in several directions a theorem about hypercyclicity of certain infinite order linear differential operators with constant coefficients and study the corresponding property for certain kinds of “antidifferential” operators which are introduced in the paper. In addition, the existence of hypercyclic functions for certain sequences of differential operators with additional properties, for instance, boundedness or with some nonvanishing derivatives, is established. |
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