10 citations · 12 across the 7 of their papers we have counts for
11 papers
Existence and non-existence in common hypercyclicity and its frequent variants
Romuald Ernst, Fernando Vieira Costa Junior, Monia Mestiri +1
Given a family of bounded linear operators acting on the same -space and indexed by a set of parameters , , we ex…
Hypercyclicity and Lipschitz-free operators
Christian Cobollo, Romuald Ernst, Quentin Menet +1
We study linearizations of dynamical systems and some of its topological properties. Special attention is paid to the case of Lipschitz-free operators, and they are shown to model…
Common frequent hypercyclicity
Stéphane Charpentier, Romuald Ernst, Monia Mestiri +1
We provide with criteria for a family of sequences of operators to share a frequently universal vector. These criteria are variants of the classical Frequent Hypercyclicity Criteri…
-Frequent hypercyclicity notions and related weighted densities
Romuald Ernst, Céline Esser, Quentin Menet
We study dynamical notions lying between -frequent hypercyclicity and reiterative hypercyclicity by investigating weighted upper densities between the unweighted upper…
Hypercyclic Algebras for convolution operators of unimodular constant term
J. Bes, R. Ernst, A. Prieto
We study the existence of hypercyclic algebras for convolution operators on the space of entire functions whose symbol has unimodular constant term. In particular, we pr…
Frequent universality criterion and densities
Romuald Ernst, A Mouze
We improve a recent result by giving the optimal conclusion possible both to the frequent universality criterion and the frequent hypercyclicity criterion using the notion of A-den…
Hypercyclic subsets
S. Charpentier, R. Ernst
We completely characterize the finite dimensional subsets A of any separable Hilbert space for which the notion of A-hypercyclicity coincides with the notion of hypercyclicity, whe…
A quantitative interpretation of the frequent hypercyclicity criterion
Romuald Ernst, A Mouze
We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessari…
Γ-supercyclicity
Stéphane Charpentier, Romuald Ernst, Quentin Menet
We characterize the subsets of $\C$ for which the notion of -supercyclicity coincides with the notion of hypercyclicity, where an operator on a Banach space is said…
-supercyclic and strongly -supercyclic operators in finite dimensions
Romuald Ernst
We prove that on , there is no -supercyclic operator with i.e. if has an dimensional subspace whose orbi…
Strongly -supercyclic operators
Romuald Ernst
In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly -supercyclic operators. This notion is stronger t…