English

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.

Keywords

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}
}
R2 v1 2026-06-23T13:51:19.365Z