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Artículo
The set of space-filling curves: topological and algebraic structure
(Elsevier, 2015-02-15)
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 ...
Artículo
Vector spaces of non-extendable holomorphic functions
(Springer, 2018-02)
In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that are not analytically continuable beyond the boundary of G is analyzed. We prove that He(G) contains, ...
Artículo
Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)
(Elsevier, 2019-04-01)
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 ...
Artículo
Banach spaces of universal Taylor series in the disc algebra
(Springer, 2016-09)
It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies that, for many small subsets E of the unit circle T, the restrictions to T of the partial sums of ...
Artículo
Linear subsets of nonlinear sets in topological vector spaces
(American Mathematical Society, 2014-01)
For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying ...
Artículo
Lineability criteria, with applications
(Elsevier, 2014-03-15)
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed ...
Artículo
[S]-linear and convex structures in function families
(Elsevier, 2019-10-15)
In this paper, the notion of [S]-lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a general abstract setting. This new notion is, then, applied to specific situations, as for instance, ...
Artículo
Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces
(Springer, 2018-06)
We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose non-null functions are nowhere differentiable at the boundary. Infinitely generated free ...
Artículo
Nowhere hölderian functions and Pringsheim singular functions in the disc algebra
(Springer, 2019-04)
We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach spaces in the disc algebra all of whose nonzero members are not α-h¨olderian at any point of the ...
Artículo
Large subspaces of compositionally universal functions with maximal cluster sets
(Elsevier, 2012-02)
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 ...