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We characterize those composition operators defined on spaces of holomorphic functions of several variables which are power bounded, i.e. the orbits of all the elements are bounded. This condition is equivalent to the composition operator being mean ergodic. We also describe the form of the symbol when the composition operator is mean ergodic.
We unify and extend several results on the dynamic behaviour of composition operators on the space of holomorphic functions on a simply connected plane domain and endowed with the compact open topology. In particular, we show that a composition operator is weakly supercyclic if and only if the algebra it generates consists entirely, except for the null one, of operators that are topologically mixing,...
We study Banach spaces of harmonic functions on open sets of $$\mathbb R ^{N}$$ or $$\mathbb C ^N$$ endowed with weighted supremum norms. We investigate the harmonic associated weight defined naturally as the analogue of the holomorphic associated weight introduced by Bierstedt, Bonet, and Taskinen and we compare them. We study composition operators with holomorphic symbol between weighted...
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