Power boundedness and related properties for weighted composition operators on S(R)
[EN] We characterize those pairs of smooth mappings for which the corresponding weighted composition operator acts continuously on . Additionally, we give several easy-to-check necessary and sufficient conditions of this property for interesting special cases. Moreover, we characterize power bounded...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/213118 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/213118 |
| Access Level: | acceso abierto |
| Palabra clave: | Weighted composition operator Power bounded operator Mean ergodic operator Space of rapidly decreasing smooth functions MATEMATICA APLICADA |
| Sumario: | [EN] We characterize those pairs of smooth mappings for which the corresponding weighted composition operator acts continuously on . Additionally, we give several easy-to-check necessary and sufficient conditions of this property for interesting special cases. Moreover, we characterize power boundedness and topologizablity of on in terms of . Among other things, as an application of our results we show that for a univariate polynomial ¿ with , power boundedness of on for every only depends on ¿ and that in this case power boundedness of is equivalent to converging to 0 in as well as to the uniform mean ergodicity of . Additionally, we give an example of a power bounded and uniformly mean ergodic weighted composition operator on for which neither the multiplication operator nor the composition operator acts on . Our results complement and considerably extend various results of Fernández, Galbis, and the second named author. |
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