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...

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Detalles Bibliográficos
Autores: Conejero, J. Alberto|||0000-0003-3681-7533, Mundayadan, A., Seoane-Sepúlveda, J. B.
Tipo de recurso: artículo
Fecha de publicación:2019
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:10251/159145
Acceso en línea:https://riunet.upv.es/handle/10251/159145
Access Level:acceso abierto
Palabra clave:Césaro integral operator
Frequent hypercyclicity
Hypercyclic operator
Linear dynamics
MATEMATICA APLICADA
Descripción
Sumario:[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.