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1 results

Growth of hypercyclic functions: a continuous path between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity
Part of
Augustin Mouze, Vincent Munnier
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 3 / August 2024

Published online by Cambridge University Press:

08 May 2024, pp. 794-829
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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.