Dynamics of multidimensional Césaro operators

Abstract

[EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 = 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.The first author was supported by MEC, grant MTM201675963-P. The third author was supported by grant MTM2015-65825-P.Conejero, JA.; Mundayadan, A.; Seoane-Sepúlveda, JB. (2019). Dynamics of multidimensional Césaro operators. Bulletin of the Belgian Mathematical Society Simon Stevin. 26(1):11-20. http://hdl.handle.net/10251/159145S112026