Poisson equation and discrete one-sided Hilbert transform for (c,a)-bounded operators

Abadias, L. (Universidad de Zaragoza) ; Galé, J. E. (Universidad de Zaragoza) ; Lizama, C.

Resumen: We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for (C, α)-bounded operators, α > 0. This extends known results for power bounded operators to the setting of Cesàro bounded operators of fractional order, thus generalizing the results substantially. In passing, we obtain a generalization of the mean ergodic theorem in our framework. Examples are given to illustrate the theory.

Idioma: Inglés

DOI: 10.1007/s11856-022-2353-z

Año: 2023

Publicado en: Israel Journal of Mathematics 253 (2023), 917–987
ISSN: 0021-2172

Factor impacto JCR: 0.8 (2023)

Categ. JCR: MATHEMATICS rank: 178 / 489 = 0.364 (2023) - Q2 - T2

Factor impacto CITESCORE: 1.7 - Mathematics (all) (Q2)

Factor impacto SCIMAGO: 0.943 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E26-17R
Financiación: info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00
Financiación: info:eu-repo/grantAgreement/ES/UZ/JIUZ-2019-CIE-01

Tipo y forma: Article (Published version)

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