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Algebrable sets of hypercyclic vectors for convolution operators

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Abstract

We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff’s operator also has this property on the space of complex-valued smooth functions on the real line.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Juan Bès

  2. Université Clermont Auvergne, CNRS, LMBP, F-63000, Clermont Ferrand, France

    Dimitris Papathanasiou

Authors
  1. Juan Bès
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  2. Dimitris Papathanasiou
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Corresponding author

Correspondence to Juan Bès.

Additional information

Dedicated to Joe Diestel and Victor Lomonosov

This work is supported in part byMEC, Project MTM 2016-7963-P. We also thank Fedor Nazarov and an anonymous referee for key observations for Section 2.

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Bès, J., Papathanasiou, D. Algebrable sets of hypercyclic vectors for convolution operators. Isr. J. Math. 238, 91–119 (2020). https://doi.org/10.1007/s11856-020-2024-x

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  • DOI: https://doi.org/10.1007/s11856-020-2024-x

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