Now showing items 1-10 of 10
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 ...
Dense-lineability of sets of Birkhoff-universal functions with rapid decay [Article]
Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear ...
Infinite dimensional holomorphic non-extendability and algebraic genericity [Article]
In this note, the linear structure of the family He(G) of holomorphic functions in a domain G of a complex Banach space that are not holomorphically continuable beyond the boundary of G is analyzed. More particularly, we ...
Hypercyclic algebras for D-multiples of convolution operators [Article]
(American Mathematical Society, 2019-02)
It is shown in this short note the existence, for each nonzero member of the ideal of D-multiples of convolution operators acting on the space of entire functions, of a scalar multiple of it supporting a hypercyclic algebra.
The set of space-filling curves: topological and algebraic structure [Article]
In this paper, a study of topological and algebraic properties of two families of functions from the unit interval I into the plane R2 is performed. The first family is the collection of all Peano curves, that is, of those ...
A dynamical characterization of sub-Arakelian subsets [Article]
We are going to characterize those sets which can be covered by an Arakelian set in terms of dynamical properties of entire functions via similarities. Moreover, if we consider the set of universal entire functions via ...
Large algebras of singular functions vanishing on prescribed sets [Article]
In this paper, the non-vacuousness of the family of all nowhere analytic infinitely differentiable functions on the real line vanishing on a prescribed set Z is characterized in terms of Z. In this case, large algebraic ...
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 ...
Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X) [Article]
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both ...
Subspaces of frequently hypercyclic functions for sequences of composition operators. [Article]
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such a criterion improves some already known ...