On the Recurrent C0-Semigroups, Their Existence, and Some Criteria

Mansooreh Moosapoor and Tuncer Acar

Journal of Mathematics, 2021, vol. 2021, 1-7

Abstract: In this paper, recurrent C0-semigroups are introduced and investigated. It is proved that, despite hypercyclic C0-semigroups, recurrent C0-semigroups can be found on finite-dimensional Banach spaces. Some criteria are stated for recurrence, which is based on open sets, neighborhoods of zero, and special eigenvectors. It is established that having a dense set of recurrent vectors is a sufficient and necessary condition for a C0-semigroup to be recurrent. Moreover, the direct sum of recurrent C0-semigroups is investigated.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6756908

DOI: 10.1155/2021/6756908

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