Dynamics of multidimensional Césaro operators
[EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 < p < infinity, and n >= 2, that is defined as C(f)(x(1),...,x(n)) = 1/x(1)x(2)...x(n) integral(x1)(0) ... integral(x1)(0) f(u(1),...,u(n))du(1)...du(n) f...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/159145 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/159145 |
| Access Level: | acceso abierto |
| Palavra-chave: | Césaro integral operator Frequent hypercyclicity Hypercyclic operator Linear dynamics MATEMATICA APLICADA |
| Resumo: | [EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 < p < infinity, and n >= 2, that is defined as C(f)(x(1),...,x(n)) = 1/x(1)x(2)...x(n) integral(x1)(0) ... integral(x1)(0) f(u(1),...,u(n))du(1)...du(n) for f is an element of L-p(I-n). This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic. |
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