Now showing items 1-10 of 24
Compositional universality in the N-dimensional ball [Article]
(De Gruyter, 2007-05)
It is proved in this note that a sequence of automorphisms on the N-dimensional unit ball acts properly discontinuously if and only if its corresponding sequence of composition operators is universal on the Hardy space of ...
Compositional hypercyclicity equals supercyclicity [Article]
(University of Houston, 2007)
In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected domain strictly contained in the complex plane is hypercyclic –that is, possesses some dense orbit– ...
On universality of composition operators in several variables [Article]
(University of Houston, 2001)
In this paper we characterize the universality of a sequence of composition operators generated by automorphisms of the N-dimensional unit polydisc DN, on Hardy spaces of DN . In addition, we provide suitable conditions ...
Maximal cluster sets along arbitrary curves [Article]
The existence of a dense linear manifold of holomorphic functions on a Jordan domain having except for zero maximal cluster set along any curve tending to the boundary with nontotal oscillation value set is shown.
Holomorphic operators generating dense images [Article]
The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane such that T f has dense images on certain subsets of G, where T is a continuous linear operator, is ...
Strongly omnipresent integral operators [Article]
An operator T on the space H(G) of holomorphic functions on a domain G is strongly omnipresent whenever there is a residual set of functions f ∈ H(G) such that T f exhibits an extremely “wild” behaviour near the boundary. ...
Monsters in Hardy and Bergman spaces [Article]
(Taylor & Francis, 2002)
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In ...
Operators with dense images everywhere [Article]
In this paper, the authors introduce the dense-image operators T as those with a wild behaviour near of the boundary of a domain G, via certain subsets. The relationship with other kinds of operators with wild behaviour ...
Boundary-chaotic behaviour of continuous functions under the action of operators [Article]
(Cambridge University Press, 2003-06)
In this paper we introduce two classes of operators on spaces of continuous functions with values in F-spaces under the action of which many functions behave chaotically near the boundary. Several examples, including ...
Maximal cluster sets of L-analytic functions along arbitrary curves [Article]
Let Ω be a domain in the N-dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose members belong to a certain class of operators defined on the space of L-analytic functions on Ω. ...