Frequently hypercyclic random vectors for C0-semigroups

Agneessens, Kevin

doi:10.1017/etds.2026.10274

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Article (Scientific journals)

Frequently hypercyclic random vectors for C0-semigroups

Agneessens, Kevin

2026 • In Ergodic Theory and Dynamical Systems, 46 (5), p. 1125 - 1154

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https://hdl.handle.net/20.500.12907/56229

DOI
10.1017/etds.2026.10274

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Keywords :

ergodic theory; frequent hypercyclicity; semigroup of operators; stochastic integral; Mathematics (all); Applied Mathematics

Abstract :

[en] We show that, under certain conditions, a strongly continuous semigroup admits an almost surely frequently hypercyclic random vector defined as a stochastic integral in Fréchet spaces with respect to the Brownian motion. Two criteria are given. We will apply the second criterion to three examples: translation semigroups on spaces of integrable functions, the exponential of weighted shifts, and the translation operators on the space of entire functions. This last example, with a stochastic approach, seems to be new in the literature. Some other examples are given.

Disciplines :

Mathematics

Author, co-author :

Agneessens, Kevin ; Université de Mons - UMONS > Faculté des Sciences > Service d'Analyse fonctionnelle

Language :

English

Title :

Frequently hypercyclic random vectors for C0-semigroups

Publication date :

May 2026

Journal title :

Ergodic Theory and Dynamical Systems

ISSN :

0143-3857

eISSN :

1469-4417

Publisher :

Cambridge University Press

Volume :

Issue :

Pages :

1125 - 1154

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0143385726102740

Research unit :

S844 - Analyse fonctionnelle

Research institute :

Complexys

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi UMONS :

since 29 May 2026

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