2025/03/01 by Shengnan He, He, Shengnan, Zongbin Yin +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2503.00542
openalex publication_date 2025/03/01 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
In this paper, we study frequent hypercyclicity for strongly continuous semigroups of operators \Tt\t∈Δ indexed with complex sectors. We propose a revised and more natural definition of frequent hypercyclicity compared to the one in [Chaouchi et al.,2020]. Additionally, we establish a sufficient condition and a necessary condition for a C0-semigroup \Tt\t ∈ Δ to be frequently hypercyclic. Moreover, we derive a practical and applicable criterion for translation semigroups \Tt\t ∈ Δ on Lpρ(Δ, \mathbbK) spaces, expressed in terms of the integral of the weight function. As a result, we provide explicit examples of frequently hypercyclic translation semigroups on Lpρ(Δ, \mathbbK). Lastly, we present a necessary condition on the weight function for the translation semigroups, under which it is demonstrated that Example I (i) [Chaouchi,2020] is not frequently hypercyclic under the revised definition.