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Artículo
Large algebras of singular functions vanishing on prescribed sets
(Springer, 2016-06-21)
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 ...
Artículo
Algebraic genericity of strict-order integrability
(Polish Academy of Sciences, Institute of Mathematics, 2010)
We provide sharp conditions on a measure µ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space Lp (µ, X) (p ≥ 1) which are not integrable with order q for any q > p (or any q < ...
Artículo
Peano curves on topological vector spaces
(Elsevier, 2014-11-01)
The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from ...
Artículo
Compositionally universal entire functions on the plane and the punctured plane
(Springer, 2013-06)
Necessary/sufficient conditions for a sequence of automorphisms of the complex plane to generate a sequence of composition operators that is universal on the punctured plane are provided. As a consequence, it is derived ...
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
Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator
(Springer, 2016)
For the Dunkl operator Λα (α > −1/2) on the space of entire functions on the complex space C, the critical rate of growth for the integral means Mp(f, r) of their hypercyclic functions f is obtained. The rate of growth of ...
Artículo
Dense-lineability of sets of Birkhoff-universal functions with rapid decay
(Elsevier, 2010-03-01)
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 ...
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 ...