Author profile: Bernal González, Luis
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Name  Bernal González, Luis 
Department  Análisis Matemático 
Knowledge area  Análisis Matemático 
Professional category  Catedrático de Universidad 
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Publications 

Final Degree Project
Las funciones Gamma de EulerGauss y Zeta de Riemann
(20200601)
The Swiss mathematician Leonhard Euler started the study of the Gamma function when he became interested in the problem ... 
Article
[S]linear and convex structures in function families
(Elsevier, 20191015)
In this paper, the notion of [S]lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a ... 
Article
Universality of sequences of operators related to Taylor series
(Elsevier, 20190601)
In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic ... 
Article
Structural aspects of the nonuniformly continuous functions and the unbounded functions within C(X)
(Elsevier, 20190401)
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, ... 
Article
Nowhere hölderian functions and Pringsheim singular functions in the disc algebra
(Springer, 20190401)
We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach ... 
Article
Subspaces of frequently hypercyclic functions for sequences of composition operators.
(Springer, 20190201)
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a ... 
Article
Hypercyclic algebras for Dmultiples of convolution operators
(American Mathematical Society, 20190201)
It is shown in this short note the existence, for each nonzero member of the ideal of Dmultiples of convolution operators acting on the space of entire functions, of a scalar multiple of it supporting a hypercyclic algebra. 
Article
Simultaneous universality
(Elsevier, 20180801)
In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously ... 
Article
Boundarynonregular functions in the disc algebra and in holomorphic Lipschitz spaces
(Springer, 20180601)
We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc ... 
Article
Highly tempering infinite matrices
(Springer, 20180401)
In this short note, it is proved the existence of infinite matrices that not only preserve convergence and limits of ... 
Article
Vector spaces of nonextendable holomorphic functions
(Springer, 20180201)
In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that ... 
Article
NonLipschitz differentiable functions on slit domains
(Springer, 20170501)
It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free ... 
Article
Infinite dimensional holomorphic nonextendability and algebraic genericity
(Elsevier, 20170115)
In this note, the linear structure of the family He(G) of holomorphic functions in a domain G of a complex Banach space ... 
Article
The algebraic size of the family of injective operators
(De Gruyter Open, 20170101)
In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of onetoone operators ... 
Article
Lineability in sequence and function spaces
(Polish Academy of Sciences, Institute of Mathematics, 20170101)
It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free ... 
Article
Banach spaces of universal Taylor series in the disc algebra
(Springer, 20160901)
It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies ... 
Article
Large algebras of singular functions vanishing on prescribed sets
(Springer, 20160621)
In this paper, the nonvacuousness of the family of all nowhere analytic infinitely differentiable functions on the real ... 
Article
Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator
(Springer, 20160101)
For the Dunkl operator Λα (α > −1/2) on the space of entire functions on the complex space C, the critical rate of growth ... 
Article
Order of growth of distributional irregular entire functions for the differentiation operator
(Taylor & Francis, 20160101)
We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. ... 
Article
The set of spacefilling curves: topological and algebraic structure
(Elsevier, 20150215)
In this paper, a study of topological and algebraic properties of two families of functions from the unit interval I into ... 
Presentation
Lineability of holomorphic nonextendability
(20150101)

Article
Peano curves on topological vector spaces
(Elsevier, 20141101)
The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval ... 
Article
Lineability criteria, with applications
(Elsevier, 20140315)
Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A ... 
Article
Linear subsets of nonlinear sets in topological vector spaces
(American Mathematical Society, 20140101)
For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear ... 
Article
Compositionally universal entire functions on the plane and the punctured plane
(Springer, 20130601)
Necessary/sufficient conditions for a sequence of automorphisms of the complex plane to generate a sequence of composition ... 
Article
Families of strongly annular functions: linear structure
(Springer, 20130101)
A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles ... 
Article
On the growth of zerofree MacLaneuniversal entire functions
(Elsevier, 20120901)
We show that exponential growth is the critical discrete rate of growth for zerofree entire functions which are universal ... 
Article
Large subspaces of compositionally universal functions with maximal cluster sets
(Elsevier, 20120201)
Let (φn) be a sequence of holomorphic selfmaps of a Jordan domain G in the complex plane. Under appropriate conditions ... 
Presentation
Universality and lineability: new trends
(20120101)

Article
Denselineability of sets of Birkhoffuniversal functions with rapid decay
(Elsevier, 20100301)
Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an ... 
Article
Compositional frequent hypercyclicity on weighted Dirichlet spaces
(The Belgian Mathematical Society, 20100201)
It is proved that, in most cases, a scalar multiple of a linearfractional generated composition operator λCϕ acting on a ... 
Article
Algebraic genericity of strictorder integrability
(Polish Academy of Sciences, Institute of Mathematics, 20100101)
We provide sharp conditions on a measure µ defined on a measurable space X guaranteeing that the family of functions in ... 
Article
Common hypercyclic functions for multiples of convolution and nonconvolution operators
(American Mathematical Society, 20091101)
We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every nonzero scalar ... 
Article
Universal Taylor series with maximal cluster sets
(Consejo Superior de Investigaciones Científicas, 20090601)
We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, ... 
Article
Interpolation by hypercyclic functions for differential operators
(Elsevier, 20090401)
We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having ... 
Article
Universal functions with prescribed zeros and interpolation properties
(University of Michigan, 20090101)

Article
Large linear manifolds of noncontinuable boundaryregular holomorphic functions
(Elsevier, 20080501)
We prove in this paper that if G is a domain in the complex plane satisfying adequate topological or geometrical conditions ... 
Article
Holomorphic operators generating dense images
(Springer, 20080101)
The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane ... 
Article
Compositional universality in the Ndimensional ball
(De Gruyter, 20070501)
It is proved in this note that a sequence of automorphisms on the Ndimensional unit ball acts properly discontinuously ... 
Article
Maximal cluster sets of Lanalytic functions along arbitrary curves
(Springer, 20070301)
Let Ω be a domain in the Ndimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose ... 
Article
Cyclicity of coefficient multipliers: Linear structure
(Springer, 20070301)
In this paper we characterize various kinds of cyclicity of sequences of coefficient multipliers, which are operators ... 
Article
Existence and nonexistence of hypercyclic semigroups
(American Mathematical Society, 20070301)
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any ... 
Article
Compositional hypercyclicity equals supercyclicity
(University of Houston, 20070101)
In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected ... 
Article
Hypercyclic subspaces in Fréchet spaces
(American Mathematical Society, 20060701)
In this note, we show that every infinitedimensional separable Fr´echet space admitting a continuous norm supports an ... 
Article
Linear structure of the weighted holomorphic nonextendibility
(Cambridge University Press, 20060601)
In this paper, it is proved that, for any domain G of the complex plane, there exist an infinitedimensional closed linear ... 
Article
Universality of holomorphic functions bounded on closed sets
(Elsevier, 20060301)
In this note, the existence of translationuniversal entire functions which are bounded on certain closed subsets is ... 
Article
Universal matrix transforms of holomorphic functions
(University of Houston, 20060101)
The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor ... 
Article
Interpolation by tamed entire functions
(Bulgarian Academy of Sciences, 20060101)
In this note it is constructed an entire function that interpolates a prescribed pair of sequences in the complex plane, ... 
Article
Lacunary noncontinuable boundaryregular holomorphic functions with universal properties
(National Academy of Sciences of the Republic of Armenia, 20060101)
A holomorphic function in a Jordan domain G in the complex plane is constructed with all its derivatives extending ... 
Article
Simultaneously maximal radial cluster sets
(Elsevier, 20050701)
In this paper, we show that for a wide class of operators T –including infi nite order differential operators, and ... 
Article
Backward Φshifts and universality
(Elsevier, 20050601)
In this paper we consider spaces of sequences which are valued in a topological space E and study generalized backward ... 
Article
Universal entire functions for affine endomorphisms of C N
(Elsevier, 20050515)
In this paper the affine endomorphisms of C N which support compositionally universal entire functions are completely characterized. 
Article
Universality on higher order Hardy spaces
(Cambridge University Press, 20050201)
We prove a SeidelWalshtype theorem about universality of a sequence of derivationcomposition operators generated by ... 
Article
Uoperators
(Cambridge University Press, 20050201)
Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives ... 
Article
Linear KierstSzpilrajn theorems
(Polish Academy of Sciences, Institute of Mathematics, 20050101)
We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn ... 
Article
Maximal cluster sets along arbitrary curves
(Elsevier, 20040801)
The existence of a dense linear manifold of holomorphic functions on a Jordan domain having except for zero maximal cluster set along any curve tending to the boundary with nontotal oscillation value set is shown. 
Article
Universal transforms of the geometric series under generalized Riesz methods
(Springer, 20040301)
In this paper generalized Riesz methods (R, p, M) of summability are considered. We prove that, to each open set O ⊂ C ... 
Article
Norms of hypercyclic sequences
(The European Digital Mathematics Library, 20040101)
In this note, is proved that every member of a wide class of Banach spaces supports a sequence (Tn) of operators with a ... 
Article
Boundarychaotic behaviour of continuous functions under the action of operators
(Cambridge University Press, 20030601)
In this paper we introduce two classes of operators on spaces of continuous functions with values in Fspaces under the ... 
PhD Thesis
Universalidad: Uoperadores y sucesiones de operadores diferenciales
(20030101)
A continuación se estudia la superciclicidad y se introduce la propiedad de la chiperciclicidad y chiperciclicidad por ... 
Article
Strongly omnipresent integral operators
(Springer, 20021201)
An operator T on the space H(G) of holomorphic functions on a domain G is strongly omnipresent whenever there is a residual ... 
Article
Dense linear manifolds of monsters
(Elsevier, 20021201)
In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic ... 
Article
Two hyperbolic Schwarz lemmas
(Cambridge University Press, 20020801)
In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings ... 
Article
Strongly omnipresent operators: general conditions and applications to composition operators
(Cambridge University Press, 20020601)
This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. ... 
Article
Exponential type of hypercyclic entire functions
(Springer, 20020401)
In this paper the exponential type of hypercyclic entire functions with respect to a sequence (Φn(D)) of differential ... 
Article
Monsters in Hardy and Bergman spaces
(Taylor & Francis, 20020101)
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and ... 
Article
Operators with dense images everywhere
(Elsevier, 20011101)
In this paper, the authors introduce the denseimage operators T as those with a wild behaviour near of the boundary of a ... 
Article
Multiplicative sequences for universal sequences of mappings
(The European Digital Mathematics Library, 20010101)
In this paper we study the universality of (cnTn) where (cn) is a scalar sequence and (Tn) is a universal sequence such ... 
Article
Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
(Polish Academy of Sciences, Institute of Mathematics, 20010101)
In this paper, an eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new ... 
Article
Holomorphic Tmonsters and strongly omnipresent operators
(Elsevier, 20000601)
Assume that G is a nonempty open subset of the complex plane and that T is an operator on the linear space of holomorphic ... 
Article
A SeidelWalsh theorem with linear differential operators
(Springer, 19990501)
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 ... 
Article
Holomorphic functions having large images under the action of differential operators
(Elsevier, 19990215)
We prove in this note that, given a simply connected domain G in the complex plane and a sequence of infinite order linear ... 
Article
Hypercyclic sequences of differential and antidifferential operators
(Elsevier, 19990201)
In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space ... 
Article
On universal entire functions with zerofree derivatives
(Springer, 19970401)
We prove in this note a generalization of a theorem due to G. Herzog on zerofree universal entire functions. Specifically, ... 
Article
Small entire functions with extremely fast growth
(Elsevier, 19970315)
We prove in this note that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is ... 
Article
A lot of “counterexamples” to Liouville's theorem
(Elsevier, 19960801)
We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M ... 
Article
Universal functions for taylor shifts
(Taylor & Francis, 19960101)
In this paper a new sort of operators, the Taylor shifts, is introduced. They appear as a generalization of weighted ... 
PhD Thesis
Funciones universales para operadores de composición en superficies de Riemann
(19940101)
"Esta memoria está dividida en cuatro capítulos. En el Capítulo cero de preliminares introducimos la notación y recordamos ... 
Article
Orden relativo de crecimiento de funciones enteras
(Universitat de Barcelona, 19880101)
In this paper, we essay a generalization of the classical concept of growth order of an entire function. We define the new ... 
Article
Exponente de convergencia generalizado de una sucesión compleja
(Universitat de Barcelona, 19870101)
Our aim in this paper is to give several new expressions for the kthconvergence exponent of a complex sequence, and an extension of this concept to a certain class of real functions. 
Article
Funciones con derivadas sucesivas grandes y pequeñas por doquier
(Universitat de Barcelona, 19870101)
In this paper we show that, given two double sequences of positive real numbers, α and β, the subset of all functions ... 
PhD Thesis 