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f-Frequently hypercyclic \(C_{0}\)-semigroups on complex sectors

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Abstract

We analyze f-frequently hypercyclic, q-frequently hypercyclic (\(q> 1\)), and frequently hypercyclic \(C_{0}\)-semigroups (\(q=1\)) defined on complex sectors,with values in separable infinite-dimensional Fréchet spaces. Some structural results are given for a general class of \({\mathcal F}\)-frequently hypercyclic \(C_{0}\)-semigroups, as well. We investigate generalized frequently hypercyclic translation semigroups and generalized frequently hypercyclic semigroups induced by semiflows on weighted function spaces. Several illustrative examples are presented.

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Acknowledgements

The authors would like to thank to the referee for the valuable comments and pointing out that the open problem in [13, Problem 9] was recently solved in [28].

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Authors and Affiliations

  1. Lab. de l’Energie et des Systémes Intelligents, Khemis Miliana University, 44225, Khemis Miliana, Algeria

    Belkacem Chaouchi

  2. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21125, Serbia

    Marko Kostić

  3. Department for Mathematics and Informatics, University of Novi Sad, Trg D. Obradovića 4, Novi Sad, 21000, Serbia

    Stevan Pilipović

  4. Faculty of Civil Engineering, Ss. Cyril and Methodius University, Partizanski Odredi 24, P.O. Box 560, 1000, Skopje, North Macedonia

    Daniel Velinov

Authors
  1. Belkacem Chaouchi
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  2. Marko Kostić
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  3. Stevan Pilipović
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  4. Daniel Velinov
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Correspondence to Daniel Velinov.

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Communicated by Jan Stochel.

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Chaouchi, B., Kostić, M., Pilipović, S. et al. f-Frequently hypercyclic \(C_{0}\)-semigroups on complex sectors. Banach J. Math. Anal. 14, 1080–1110 (2020). https://doi.org/10.1007/s43037-020-00053-2

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  • DOI: https://doi.org/10.1007/s43037-020-00053-2

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