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Poisson Equation and Discrete One-Sided Hilbert Transform for (C, alpha)-Bounded Operators
ISSN
0021-2172
Date Issued
2023
Author(s)
Abadias, Luciano
Gale, Jose E.
Abstract
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for (C, alpha)-bounded operators, alpha > 0. This extends known results for power bounded operators to the setting of Cesaro 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.