Abstract.
We show that no power of any entire function is hypercyclic for Birkhoff’s translation operator on \(\mathcal{H}(\mathbb{C})\). On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane’s differentiation operator is a Gδ-dense subset of \(\mathcal{H}(\mathbb{C})\).
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The second author was supported in part by GVA, grant CTESPP/2005.
The second and third authors were supported in part by MEC and FEDER, Project MTM2004-02262 and Research Net MTM2006-26627-E.
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Aron, R.M., Conejero, J.A., Peris, A. et al. Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators. Integr. equ. oper. theory 58, 591–596 (2007). https://doi.org/10.1007/s00020-007-1490-4
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DOI: https://doi.org/10.1007/s00020-007-1490-4