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Growth of hypercyclic functions: a continuous path between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity

Part of: Miscellaneous topics of analysis in the complex domain Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  08 May 2024

Augustin Mouze  and
Vincent Munnier
Augustin Mouze*
Affiliation:
CNRS, UMR 8524 - Laboratoire Paul Painlevé, École Centrale de Lille, Univ. Lille, Lille, France
Vincent Munnier
Affiliation:
Lycée Jacques Prévert, Boulogne Billancourt, France
*
Corresponding author: Augustin Mouze, email: augustin.mouze@univ-lille.fr
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Abstract

We are interested in the optimal growth in terms of Lp-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic functions on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity.

Keywords

hypercyclic vectorsweighted shiftsrate of growthboundary behaviour

MSC classification

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 30E25: Boundary value problems 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 47B38: Operators on function spaces (general)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 36
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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