CALDERÓN MORENO , María Del Carmen

Dirección General de Enseñanza Superior

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 structures are found inside such family. The results obtained complete or extend a number of previous ones by several authors.

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 result due to Beardon. A property of preserving hyperbolic distances also studied by Beardon is here completely characterized.

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 is studied, proving that the new concept generalizes the earlier of omnipresent, but there is no good relationship with the...

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 this paper the Hardy spaces Hp and the Bergman spaces Bp (1 ≤ p < ∞) on the unit disk are considered, and it is shown that...

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 strongly omnipresent operator and of T-monster, which are related to the wild behaviour of certain holomorphic functions near...

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 onto linear operators, left and right composition operators, multiplication operators, and operators with pointwise dense range...

In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic functions of a domain in the complex plane. The concept is more restrictive than that of strongly omnipresent operators, also introduced by the authors in an earlier work, and both of them are related to the existence of...

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.

Assume that {Sn}∞1 is a sequence of automorphisms of the open unit disk D and that {Tn}∞1 is a sequence of linear differential operators with constant coefficients, both of them satisfying suitable conditions. We prove that for certain spaces X of holomorphic functions in the open unit disk, the set of functions f ∈ X such that {(Tnf) ◦ Sn : n...

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 for the universality of partial derivative-composition operators in certain spaces X of holomorphic functions in DN and the...

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 similarities that are bounded on such a sub-Arakelian set, then it is shown that its algebraic size is as large as possible. As...

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 certain class of operators on presents some universal properties related to the overconvergence phenomenon.

In this note, a vector space of real-analytic functions on the plane is explicitly constructed such that all its nonzero functions are non-integrable but yet their two iterated integrals exist as real numbers and coincide. Moreover, it is shown that this vector space is dense in the space of all real continuous functions on the plane endowed...