We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for (C, α)-bounded operators, α > 0. This extends known results for power bounded operators to the setting of Cesàro bounded operators of fractional order, thus generalizing the results substantially. In passing, we obtain a generalization of the mean ergodic theorem in our framework. Examples are given to illustrate the theory.
Especialidad publicación
Tipo publicación
Poisson Equation And Discrete One-Sided Hilbert Transform For (C, Alpha)-Bounded Operators
