Now showing items 11-20 of 24
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 ...
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– ...
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 ...
Universal functions with small derivatives and extremely fast growth [Article]
(De Gruyter, 2002-03)
Universal Taylor series with maximal cluster sets [Article]
(Consejo Superior de Investigaciones Científicas, 2009-06)
We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, so connecting outer wild behavior to inner wild behavior. Specifically, it is proved the existence ...
Universal matrix transforms of holomorphic functions [Article]
(University of Houston, 2006)
The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor series at points outside their disk of convergence. During the seventies Chui and Parnes and the ...
Lacunary non-continuable boundary-regular holomorphic functions with universal properties [Article]
(National Academy of Sciences of the Republic of Armenia, 2006)
A holomorphic function in a Jordan domain G in the complex plane is constructed with all its derivatives extending continuously up to the boundary G that happens to be a natural boundary of In addition the action of a ...
Universality on higher order Hardy spaces [Article]
(Cambridge University Press, 2005-02)
We prove a Seidel-Walsh-type theorem about universality of a sequence of derivation-composition operators generated by automorphisms of the unit disk in the setting of the higher order Hardy spaces. Moreover, some related ...
Holomorphic T-monsters and strongly omnipresent operators [Article]
Assume that G is a nonempty open subset of the complex plane and that T is an operator on the linear space of holomorphic functions in G, endowed with the compact-open topology. In this paper we introduce the notions of ...
Two hyperbolic Schwarz lemmas [Article]
(Cambridge University Press, 2002-08)
In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings on the unit disk with fixed multiplicity for the zero at the origin, hence extending a recent ...