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On the set of hypercyclic vectors for the differentiation operator

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Abstract

Let D be the differentiation operator Df = f′ acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

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Authors and Affiliations

  1. Department of Pure Mathematics, Queens’s University Belfast, University Road, Belfast, BT7 1NN, UK

    Stanislav Shkarin

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  1. Stanislav Shkarin
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Correspondence to Stanislav Shkarin.

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Shkarin, S. On the set of hypercyclic vectors for the differentiation operator. Isr. J. Math. 180, 271–283 (2010). https://doi.org/10.1007/s11856-010-0104-z

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  • DOI: https://doi.org/10.1007/s11856-010-0104-z

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