Resumen:
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[EN] Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We ...[+]
[EN] Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the corresponding notion of hypercyclicity, the influence of power boundedness, and the interplay between recurrence and spectral properties. We obtain, in particular, Ansari-and Leon-Muller-type theorems for F-recurrence under very weak assumptions on the Furstenberg family F. This allows us, as a by-product, to deduce Ansari-and Leon-Muller-type theorems for F-hypercyclicity
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Código del Proyecto:
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/
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info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/
info:eu-repo/grantAgreement/MICIU//FPU19%2F04094//AYUDA PREDOCTORAL FPU-LOPEZ MARTINEZ. PROYECTO: TEORÍA COMBINATORIA DE NÚMEROS, RECURRENCIA DE OPERADORES Y DINÁMICA LINEAL/
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//PROMETEO%2F2021%2F070//Análisis funcional, dinámica de operadores y aplicaciones/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102//ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/
info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P//Dinámica de operadores/
info:eu-repo/grantAgreement/FNRS//PDR T.0164.16/
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Agradecimientos:
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The work was partially supported by MCIN/AEI/10.13039/501100011033, Projects PID2019-105011GBI00 and MTM2016-75963-P; the second author was also supported by FNRS Grant PDR T.0164.16; the third author was supported the ...[+]
The work was partially supported by MCIN/AEI/10.13039/501100011033, Projects PID2019-105011GBI00 and MTM2016-75963-P; the second author was also supported by FNRS Grant PDR T.0164.16; the third author was supported the Ministry of Education of Spain (grant FPU2019/04094); the fourth author was also supported by Generalitat Valenciana, Projects PROMETEO/2017/102 and PROMETEU/2021/070.
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