23 citations · 67 across the 10 of their papers we have counts for
11 papers
-Frequently Hypercyclic Operators
Tom Carroll, Clifford Gilmore
The concept of -frequent hypercyclicity is introduced in order to provide a refined form of frequent hypercyclicity. This is achieved by replacing the denominator in the definit…
Approximation numbers of differences of composition operators
Frédéric Bayart, Clifford Gilmore, Sibel Sahin
In this study we consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H 2 (D). We obtain both upper and lower bounds for the…
Interactions between Universal Composition Operators and Complex Dynamics
Vasiliki Evdoridou, Clifford Gilmore, Myrto Manolaki
This paper is concerned with universality properties of composition operators , where the symbol is given by a transcendental entire function restricted to parts of its Fa…
Typicality of operators on Fréchet algebras admitting a hypercyclic algebra
William Alexandre, Clifford Gilmore, Sophie Grivaux
This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fréchet algebras, endowed with th…
Linear Dynamical Systems
Clifford Gilmore
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, -frequent hypercyclicity, reiterativ…
Short geodesic loops and norms of eigenfunctions on large genus random surfaces
Clifford Gilmore, Etienne Le Masson, Tuomas Sahlsten +1
We give upper bounds for norms of eigenfunctions of the Laplacian on compact hyperbolic surfaces in terms of a parameter depending on the growth rate of the number of short g…
Weighted composition operators on Fock spaces and their dynamics
Tom Carroll, Clifford Gilmore
Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent th…
Rate of Growth of Distributionally Chaotic Functions
Clifford Gilmore, Félix Martínez-Giménez, Alfred Peris
We investigate the permissible growth rates of functions that are distributionally chaotic with respect to differentiation operators. We improve on the known growth estimates for $…
Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator
Clifford Gilmore, Eero Saksman, Hans-Olav Tylli
We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on , that is frequently hypercyclic with respect to the par…
Hypercyclicity Properties of Commutator Maps
Clifford Gilmore, Eero Saksman, Hans-Olav Tylli
We investigate the hypercyclic properties of commutator maps acting on separable ideals of operators. As the main result we prove the commutator map induced by scalar multiples of…
Dynamics of Generalised Derivations and Elementary Operators
Clifford Gilmore
We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We al…