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arXiv · 2002.10122

Poisson equation and discrete one-sided Hilbert transform for $(C,\alpha)$-bounded operators

Luciano Abadias·José E. Galé·Carlos Lizama
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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.

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Luciano Abadias, José E. Galé, Carlos Lizama. 2020-02-24. Poisson equation and discrete one-sided Hilbert transform for $(C,\alpha)$-bounded operators. https://arxiv.org/abs/2002.10122

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