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weighted densities

Ergodic Theory and Dynamical Systems (1)

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1 results

Frequent universality criterion and densities
Part of
- Topological dynamics
- General theory of linear operators
R. ERNST, A. MOUZE
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 3 / March 2021

Published online by Cambridge University Press:

25 November 2019, pp. 846-868

Print publication:

March 2021
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We improve a recent result by giving the optimal conclusion both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of $A$-densities, where $A$ refers to some weighted densities sharper than the natural lower density. Moreover, we construct an operator which is logarithmically frequently hypercyclic but not frequently hypercyclic.