Dynamics of composition operators in analytic functional Hilbert spaces. (Dinámica de operadores de composición en espacios de Hilbert funcionales analíticos.)
Dynamics of differentiation and integration operators on weighted spaces of entire functions
We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study their spectra. Special emphasis is put on exponential weights.
Dynamics of differentiation operators on generalized weighted Bergman spaces
The chaos of the differentiation operator on generalized weighted Bergman spaces of entire functions has been characterized recently by Bonet and Bonilla in [CAOT 2013], when the differentiation operator is continuous. Motivated by those, we investigate conditions to ensure that finite many powers of differentiation operators are disjoint hypercyclic on generalized weighted Bergman spaces of entire functions.