THE RECURRENT HYPERCYCLICITY CRITERION FOR TRANSLATION C0-SEMIGROUPS ON COMPLEX SECTORS

Let $\{T_t\}_{t\in \Delta}$ be the translation semigroup with a sector $\Delta\subset \mathbb{C}$ as index set. The recurrent hypercyclicity criterion (RHCC) for the $C_0$-semigroup $\{T_t\}_{t\in \Delta}$ is established, and then the equivalent conditions ensuring $\{T_t\}_{t\in \Delta}$ satisfying...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2023, 60(2), , pp.293-305
Main Authors: Yu-Xia Liang, Zhi-Yuan Xu, Ze-Hua Zhou
Format: Article
Language:English
Subjects:
수학
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Summary:Let $\{T_t\}_{t\in \Delta}$ be the translation semigroup with a sector $\Delta\subset \mathbb{C}$ as index set. The recurrent hypercyclicity criterion (RHCC) for the $C_0$-semigroup $\{T_t\}_{t\in \Delta}$ is established, and then the equivalent conditions ensuring $\{T_t\}_{t\in \Delta}$ satisfying the RHCC on weighted spaces of $p$-integrable and of continuous functions are presented. Especially, every chaotic semigroup $\{T_t\}_{t\in \Delta}$ satisfies the RHCC. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b210802