Bulletin of the Korean Mathematical Society (대한수학회보)

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

  • Yuxia Liang (School of Mathematical Sciences Tianjin Normal University) ;
  • Zhi-Yuan Xu (School of Mathematics Tianjin University) ;
  • Ze-Hua Zhou (School of Mathematics Tianjin University)
  • Received : 2021.11.03
  • Accepted : 2023.01.26
  • Published : 2023.03.31
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Abstract

Let {Tt}t∈∆ be the translation semigroup with a sector ∆ ⊂ ℂ as index set. The recurrent hypercyclicity criterion (RHCC) for the C0-semigroup {Tt}t∈∆ is established, and then the equivalent conditions ensuring {Tt}t∈∆ satisfying the RHCC on weighted spaces of p-integrable and of continuous functions are presented. Especially, every chaotic semigroup {Tt}t∈∆ satisfies the RHCC.

Keywords

Acknowledgement

The first author was supported in part by the National Natural Science Foundation of China Grant #11701422. The second author was supported in part by the National Natural Science Foundation of China Grant #12271396. The third author was supported in part by the National Natural Science Foundation of China Grant #12171353.

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