Convergence rates in mean ergodic theorems for Cesàro bounded operators

Abadías Ullod, Luciano (Universidad de Zaragoza) ; Galé, José E. (Universidad de Zaragoza)

Resumen: We establish the (polynomially) logarithmic decay of ergodic means of Cesàro bounded operators of any fractional order, under convergence of the one-sided ergodic Hilbert transform. This extends the theorem of Gomilko, Haase and Tomilov for power bounded operators. We also improve the polynomial decay of means involved in the fractional Poisson equation. The theorems are obtained as an application of a general result, also proved here, about rates of decay of means for Cesàro bounded operators.

Idioma: Inglés

DOI: 10.1007/s44146-025-00189-3

Año: 2025

Publicado en: Acta Scientiarum Mathematicarum (2025), [34 pp.]
ISSN: 0001-6969

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/MICIU/PID2022-137294NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)