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Powers of hypercyclic functions for some classical hypercyclic operators

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Aron, Richard M. and Conejero, Jose A. and Seoane-Sepúlveda, Juan B. (2007) Powers of hypercyclic functions for some classical hypercyclic operators. Integral Equations and Operator Theory, 58 (4). pp. 591-596. ISSN 0378-620X

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs00020-007-1490-4



Abstract

We show that no power of any entire function is hypercyclic for Birkhoff's translation operator on H(C). On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane's differentiation operator is a G(delta)-dense subset of H(C).


Item Type:Article
Uncontrolled Keywords:Hypercyclic vectors; Universal functions.
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20076
Deposited On:22 Feb 2013 14:25
Last Modified:28 Nov 2016 08:56

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