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Strongly Mixing Convolution Operators on Fréchet Spaces of Entire Functions of a Given Type and Order

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Abstract

We show that convolution operators on certain spaces of entire functions of a given type and order on Banach spaces are strongly mixing with respect to an invariant Borel probability measure with full support (a stronger property than frequent hypercyclicity). Based on results of S. Muro, D. Pinasco and M. Savransky we also show the existence of frequently hypercyclic entire functions of exponential growth, and the existence of frequently hypercyclic subspaces for such convolution operators.

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Acknowledgements

We are very much indebted to the referee for his/her careful reading and many valuable suggestions and comments.

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Authors and Affiliations

  1. IMECC, Universidade Estadual de Campinas, Campinas, SP, CEP: 13083-859, Brazil

    Blas M. Caraballo

  2. Faculdade de Matemática, Universidade Federal de Uberlândia, Uberlândia, MG, Cep: 38.400-902, Brazil

    Vinícius V. Fávaro

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  1. Blas M. Caraballo
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  2. Vinícius V. Fávaro
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Correspondence to Blas M. Caraballo.

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Blas M. Caraballo was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brasil (CAPES) - Finance Code 001 and in part by CNPq. Vinícius V. Fávaro is supported by FAPEMIG Grant PPM-00217-18; and CNPq Grant 310500/2017-6.

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Caraballo, B.M., Fávaro, V.V. Strongly Mixing Convolution Operators on Fréchet Spaces of Entire Functions of a Given Type and Order. Integr. Equ. Oper. Theory 92, 31 (2020). https://doi.org/10.1007/s00020-020-02589-2

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