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Frequent hypercyclicity of weighted composition operators on the space of smooth functions

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Abstract

We prove that every hypercyclic weighted composition operator acting on the space of smooth functions on the real line is already frequently hypercyclic. Moreover, for a given frequently hypercyclic weighted composition operator \(C_{w,\psi }\) we show that \(C^\infty ({\mathbb {R}})=FHC(C_{w,\psi })+FHC(C_{w,\psi })\) and that \(FHC(C_{w,\psi })\cup \{0\}\) contains a closed infinite dimensional subspace.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Ul. Uniwersytetu Poznańskiego 4, 61-614, Poznań, Poland

    Krzysztof Piszczek & Adam Przestacki

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  1. Krzysztof Piszczek
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  2. Adam Przestacki
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Correspondence to Krzysztof Piszczek.

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The research of both authors was partially supported by the National Science Centre (Poland) Grant UMO-2013/10/A/ST1/00091.

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Piszczek, K., Przestacki, A. Frequent hypercyclicity of weighted composition operators on the space of smooth functions. RACSAM 115, 51 (2021). https://doi.org/10.1007/s13398-020-00995-0

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