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pro vyhledávání: '"Gilmore, Clifford"'
This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is restricted to
Externí odkaz:
http://arxiv.org/abs/2409.16260
This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our main results show that with
Externí odkaz:
http://arxiv.org/abs/2312.08321
Autor:
Gilmore, Clifford
Publikováno v:
Irish Math. Soc. Bulletin, 86:47-77, 2020
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and distributional cha
Externí odkaz:
http://arxiv.org/abs/2007.12647
Publikováno v:
Geometric and Functional Analysis GAFA 31, 62-110 (2021)
We give upper bounds for $L^p$ 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 geodesic loops passing through a point. When the genus $g \to +\infty$,
Externí odkaz:
http://arxiv.org/abs/1912.09961
Autor:
Carroll, Tom, Gilmore, Clifford
Publikováno v:
J. Math. Anal. Appl., 502(1):125234, 2021
Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on the Fock
Externí odkaz:
http://arxiv.org/abs/1911.07254
Publikováno v:
Math. Inequal. Appl., 25(1):145-167, 2022
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 $D$-distributionally chaotic entire functions, where growth is in terms
Externí odkaz:
http://arxiv.org/abs/1810.09266
Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator
Publikováno v:
Proc. Roy. Soc. Edinburgh Sect. A, 149(6):1577-1594, 2019
We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on $\mathbb{R}^N$, that is frequently hypercyclic with respect to the partial differentiation operator $\partial/\partial x_k$ and which has a
Externí odkaz:
http://arxiv.org/abs/1708.08764
Publikováno v:
Integr. Equ. Oper. Theory, 87(1), 139-155 (2017)
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 the backward shift operator fails to be hypercyclic on the space of co
Externí odkaz:
http://arxiv.org/abs/1609.04986
Autor:
Gilmore, Clifford
Publikováno v:
Complex Anal. Oper. Theory, 13(1):257-274, 2019
We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on particular
Externí odkaz:
http://arxiv.org/abs/1605.07409
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