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

2020/02/24 by Luciano Abadías, Abadias, Luciano, Jośe E. Galé +3
Mathematics · #26A33 #40G05 #47A56 #47A60 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Primary 47A64 #Secondary 47A35 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2002.10122

openalex publication_date 2020/02/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Cesàro 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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