论文信息 - Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators

Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators

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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