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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
Holomorphic T-monsters and strongly omnipresent operators
(Elsevier, 2000-06)
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 ...
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
Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
(Polish Academy of Sciences, Institute of Mathematics, 2001)
In this paper, an eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic ...
Artículo
Orden relativo de crecimiento de funciones enteras
(Universitat de Barcelona, 1988)
In this paper, we essay a generalization of the classical concept of growth order of an entire function. We define the new parameter ρg(f), the relative growth order of f(z) with respect to g(z), which establishes a direct ...
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 ...