Now showing items 1-10 of 13
Cyclicity of coefficient multipliers: Linear structure [Article]
In this paper we characterize various kinds of cyclicity of sequences of coefficient multipliers, which are operators defined on spaces of holomorphic functions. In the case of a single coefficient multiplier we characterize ...
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 ...
Large subspaces of compositionally universal functions with maximal cluster sets [Article]
Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions on (φn), we construct an H(G)-dense linear manifold –as well as a closed infinite-dimensional ...
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.
Lineability and modes of convergence [Article]
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are ...
Algebraic structure of continuous, unbounded and integrable functions [Article]
In this paper we study the large linear and algebraic size of the family of unbounded continuous and integrable functions in [0, +∞) and of the family of sequences of these functions converging to zero uniformly on ...
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 ...
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. ...
Simultaneously maximal radial cluster sets [Article]
In this paper, we show that for a wide class of operators T –including infi- nite order differential operators, and multiplication and composition operators– acting on the space H(D) of holomorphic functions in the unit ...