Poisson equation and discrete one-sided Hilbert transform for $(C,\alpha)$-bounded operators
Functional Analysis
2020-02-25 v1
Abstract
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Ces\`aro bounded operators of fractional order. The results obtained fairly generalize the corresponding ones for power-bounded operators. In passing, we give an extension of the mean ergodic theorem. Examples are given to illustrate the theory.
Cite
@article{arxiv.2002.10122,
title = {Poisson equation and discrete one-sided Hilbert transform for $(C,\alpha)$-bounded operators},
author = {Luciano Abadias and José E. Galé and Carlos Lizama},
journal= {arXiv preprint arXiv:2002.10122},
year = {2020}
}