Data

NameBernal González, Luis
DepartmentAnálisis Matemático
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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  • Items

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  • Visits

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  Publications

 

Final Degree Project
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Las funciones Gamma de Euler-Gauss y Zeta de Riemann

Bernal González, Luis; Sánchez Cuadrado, José Manuel (2020-06-01)
The Swiss mathematician Leonhard Euler started the study of the Gamma function when he became interested in the problem ...
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[S]-linear and convex structures in function families

Bernal González, Luis; Conejero Casares, José Alberto; Murillo Arcila, Marina; Seoane Sepúlveda, Juan Benigno (Elsevier, 2019-10-15)
In this paper, the notion of [S]-lineability (originally coined by Vladimir I. Gurariy) is introduced and developed in a ...
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Universality of sequences of operators related to Taylor series

Bernal González, Luis; Cabana Méndez, Hernán Javier; Muñoz Fernández, Gustavo Adolfo; Seoane Sepúlveda, Juan Benigno (Elsevier, 2019-06-01)
In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic ...
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Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)

Ayala Gómez, Rafael; Bernal González, Luis; Calderón Moreno, María del Carmen; Vilches Alarcón, José Antonio (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, ...
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Nowhere hölderian functions and Pringsheim singular functions in the disc algebra

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; López-Salazar Codes, Jerónimo; Seoane Sepúlveda, Juan Benigno (Springer, 2019-04-01)
We prove the existence of dense linear subspaces, of infinitely generated subalgebras and of infinite dimensional Banach ...
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Subspaces of frequently hypercyclic functions for sequences of composition operators.

Bernal González, Luis; Calderón Moreno, María del Carmen; Jung, Andreas; Prado Bassas, José Antonio (Springer, 2019-02-01)
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a ...
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Hypercyclic algebras for D-multiples of convolution operators

Bernal González, Luis; Calderón Moreno, María del Carmen (American Mathematical Society, 2019-02-01)
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.
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Simultaneous universality

Bernal González, Luis; Jung, Andreas (Elsevier, 2018-08-01)
In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously ...
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Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; López-Salazar Codes, Jerónimo; Seoane Sepúlveda, Juan Benigno (Springer, 2018-06-01)
We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc ...
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Highly tempering infinite matrices

Bernal González, Luis; Conejero Casares, José Alberto; Murillo Arcila, Marina; Seoane Sepúlveda, Juan Benigno (Springer, 2018-04-01)
In this short note, it is proved the existence of infinite matrices that not only preserve convergence and limits of ...
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Vector spaces of non-extendable holomorphic functions

Bernal González, Luis (Springer, 2018-02-01)
In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that ...
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Non-Lipschitz differentiable functions on slit domains

Bernal González, Luis; Jiménez Rodríguez, Pablo; Muñoz Fernández, Gustavo Adolfo; Seoane Sepúlveda, Juan Benigno (Springer, 2017-05-01)
It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free ...
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Infinite dimensional holomorphic non-extendability and algebraic genericity

Bernal González, Luis; Calderón Moreno, María del Carmen; Seoane Sepúlveda, Juan Benigno (Elsevier, 2017-01-15)
In this note, the linear structure of the family He(G) of holomorphic functions in a domain G of a complex Banach space ...
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The algebraic size of the family of injective operators

Bernal González, Luis (De Gruyter Open, 2017-01-01)
In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators ...
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Lineability in sequence and function spaces

Araújo Soares, Gustavo; Bernal González, Luis; Muñoz Fernández, Gustavo Adolfo; Prado Bassas, José Antonio; Seoane Sepúlveda, Juan Benigno (Polish Academy of Sciences, Institute of Mathematics, 2017-01-01)
It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free ...
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Banach spaces of universal Taylor series in the disc algebra

Bernal González, Luis; Jung, Andreas; Müller, Jürgen (Springer, 2016-09-01)
It is proved that there are large vector spaces of functions in the disc algebra for which every nonzero member satisfies ...
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Large algebras of singular functions vanishing on prescribed sets

Bernal González, Luis; Calderón Moreno, María del Carmen (Springer, 2016-06-21)
In this paper, the non-vacuousness of the family of all nowhere analytic infinitely differentiable functions on the real ...
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Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 2016-01-01)
For the Dunkl operator Λα (α > −1/2) on the space of entire functions on the complex space C, the critical rate of growth ...
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Order of growth of distributional irregular entire functions for the differentiation operator

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Taylor & Francis, 2016-01-01)
We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. ...
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The set of space-filling curves: topological and algebraic structure

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (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 ...
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Lineability of holomorphic non-extendability

Bernal González, Luis (2015-01-01)
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Peano curves on topological vector spaces

Gurgel e Albuquerque, Nacib André; Bernal González, Luis; Pellegrino, Daniel M.; Seoane Sepúlveda, Juan Benigno (Elsevier, 2014-11-01)
The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval ...
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Lineability criteria, with applications

Bernal González, Luis; Ordóñez Cabrera, Manuel Hilario (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 ...
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Linear subsets of nonlinear sets in topological vector spaces

Bernal González, Luis; Pellegrino, Daniel M.; Seoane Sepúlveda, Juan Benigno (American Mathematical Society, 2014-01-01)
For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear ...
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Compositionally universal entire functions on the plane and the punctured plane

Bernal González, Luis (Springer, 2013-06-01)
Necessary/sufficient conditions for a sequence of automorphisms of the complex plane to generate a sequence of composition ...
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Families of strongly annular functions: linear structure

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 2013-01-01)
A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles ...
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On the growth of zero-free MacLane-universal entire functions

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Costakis, George (Elsevier, 2012-09-01)
We show that exponential growth is the critical discrete rate of growth for zero-free entire functions which are universal ...
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Large subspaces of compositionally universal functions with maximal cluster sets

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Elsevier, 2012-02-01)
Let (φn) be a sequence of holomorphic self-maps of a Jordan domain G in the complex plane. Under appropriate conditions ...
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Universality and lineability: new trends

Bernal González, Luis (2012-01-01)
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Dense-lineability of sets of Birkhoff-universal functions with rapid decay

Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (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 ...
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Compositional frequent hypercyclicity on weighted Dirichlet spaces

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (The Belgian Mathematical Society, 2010-02-01)
It is proved that, in most cases, a scalar multiple of a linear-fractional generated composition operator λCϕ acting on a ...
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Algebraic genericity of strict-order integrability

Bernal González, Luis (Polish Academy of Sciences, Institute of Mathematics, 2010-01-01)
We provide sharp conditions on a measure µ defined on a measurable space X guaranteeing that the family of functions in ...
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Common hypercyclic functions for multiples of convolution and non-convolution operators

Bernal González, Luis (American Mathematical Society, 2009-11-01)
We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every nonzero scalar ...
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Universal Taylor series with maximal cluster sets

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Consejo Superior de Investigaciones Científicas, 2009-06-01)
We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, ...
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Interpolation by hypercyclic functions for differential operators

Bernal González, Luis (Elsevier, 2009-04-01)
We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having ...
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Universal functions with prescribed zeros and interpolation properties

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Niess, Markus (University of Michigan, 2009-01-01)
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Large linear manifolds of non-continuable boundary-regular holomorphic functions

Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (Elsevier, 2008-05-01)
We prove in this paper that if G is a domain in the complex plane satisfying adequate topological or geometrical conditions ...
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Holomorphic operators generating dense images

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Springer, 2008-01-01)
The existence of infinite dimensional closed linear spaces of holomorphic functions f on a domain G in the complex plane ...
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Compositional universality in the N-dimensional ball

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (De Gruyter, 2007-05-01)
It is proved in this note that a sequence of automorphisms on the N-dimensional unit ball acts properly discontinuously ...
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Maximal cluster sets of L-analytic functions along arbitrary curves

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Springer, 2007-03-01)
Let Ω be a domain in the N-dimensional real space, L be an elliptic differential operator, and (Tn) be a sequence whose ...
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Cyclicity of coefficient multipliers: Linear structure

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Springer, 2007-03-01)
In this paper we characterize various kinds of cyclicity of sequences of coefficient multipliers, which are operators ...
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Existence and nonexistence of hypercyclic semigroups

Bernal González, Luis; Grosse-Erdmann, Karl-Goswin (American Mathematical Society, 2007-03-01)
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any ...
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Compositional hypercyclicity equals supercyclicity

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (University of Houston, 2007-01-01)
In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected ...
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Hypercyclic subspaces in Fréchet spaces

Bernal González, Luis (American Mathematical Society, 2006-07-01)
In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an ...
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Linear structure of the weighted holomorphic non-extendibility

Bernal González, Luis (Cambridge University Press, 2006-06-01)
In this paper, it is proved that, for any domain G of the complex plane, there exist an infinite-dimensional closed linear ...
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Universality of holomorphic functions bounded on closed sets

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Elsevier, 2006-03-01)
In this note, the existence of translation-universal entire functions which are bounded on certain closed subsets is ...
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Universal matrix transforms of holomorphic functions

Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (University of Houston, 2006-01-01)
The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor ...
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Interpolation by tamed entire functions

Bernal González, Luis (Bulgarian Academy of Sciences, 2006-01-01)
In this note it is constructed an entire function that interpolates a prescribed pair of sequences in the complex plane, ...
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Lacunary non-continuable boundary-regular holomorphic functions with universal properties

Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (National Academy of Sciences of the Republic of Armenia, 2006-01-01)
A holomorphic function in a Jordan domain G in the complex plane is constructed with all its derivatives extending ...
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Simultaneously maximal radial cluster sets

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Elsevier, 2005-07-01)
In this paper, we show that for a wide class of operators T –including infi- nite order differential operators, and ...
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Backward Φ-shifts and universality

Bernal González, Luis (Elsevier, 2005-06-01)
In this paper we consider spaces of sequences which are valued in a topological space E and study generalized backward ...
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Universal entire functions for affine endomorphisms of C N

Bernal González, Luis (Elsevier, 2005-05-15)
In this paper the affine endomorphisms of C N which support compositionally universal entire functions are completely characterized.
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Universality on higher order Hardy spaces

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (Cambridge University Press, 2005-02-01)
We prove a Seidel-Walsh-type theorem about universality of a sequence of derivation-composition operators generated by ...
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U-operators

Bernal González, Luis; Prado Tendero, José Antonio (Cambridge University Press, 2005-02-01)
Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives ...
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Linear Kierst-Szpilrajn theorems

Bernal González, Luis (Polish Academy of Sciences, Institute of Mathematics, 2005-01-01)
We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn ...
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Maximal cluster sets along arbitrary curves

Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Elsevier, 2004-08-01)
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.
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Universal transforms of the geometric series under generalized Riesz methods

Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (Springer, 2004-03-01)
In this paper generalized Riesz methods (R, p, M) of summability are considered. We prove that, to each open set O ⊂ C ...
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Norms of hypercyclic sequences

Bernal González, Luis (The European Digital Mathematics Library, 2004-01-01)
In this note, is proved that every member of a wide class of Banach spaces supports a sequence (Tn) of operators with a ...
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Boundary-chaotic behaviour of continuous functions under the action of operators

Bernal González, Luis; Calderón Moreno, María del Carmen (Cambridge University Press, 2003-06-01)
In this paper we introduce two classes of operators on spaces of continuous functions with values in F-spaces under the ...
PhD Thesis
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Universalidad: U-operadores y sucesiones de operadores diferenciales

Bernal González, Luis; Prado Tendero, José Antonio (2003-01-01)
A continuación se estudia la superciclicidad y se introduce la propiedad de la c-hiperciclicidad y c-hiperciclicidad por ...
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Strongly omnipresent integral operators

Bernal González, Luis; Calderón Moreno, María del Carmen; Grosse-Erdmann, Karl-Goswin (Springer, 2002-12-01)
An operator T on the space H(G) of holomorphic functions on a domain G is strongly omnipresent whenever there is a residual ...
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Dense linear manifolds of monsters

Bernal González, Luis; Calderón Moreno, María del Carmen (Elsevier, 2002-12-01)
In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic ...
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Two hyperbolic Schwarz lemmas

Bernal González, Luis; Calderón Moreno, María del Carmen (Cambridge University Press, 2002-08-01)
In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings ...
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Strongly omnipresent operators: general conditions and applications to composition operators

Bernal González, Luis; Calderón Moreno, María del Carmen; Grosse-Erdmann, Karl-Goswin (Cambridge University Press, 2002-06-01)
This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. ...
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Exponential type of hypercyclic entire functions

Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 2002-04-01)
In this paper the exponential type of hypercyclic entire functions with respect to a sequence (Φn(D)) of differential ...
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Monsters in Hardy and Bergman spaces

Bernal González, Luis; Calderón Moreno, María del Carmen (Taylor & Francis, 2002-01-01)
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and ...
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Operators with dense images everywhere

Bernal González, Luis; Calderón Moreno, María del Carmen (Elsevier, 2001-11-01)
In this paper, the authors introduce the dense-image operators T as those with a wild behaviour near of the boundary of a ...
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Multiplicative sequences for universal sequences of mappings

Bernal González, Luis (The European Digital Mathematics Library, 2001-01-01)
In this paper we study the universality of (cnTn) where (cn) is a scalar sequence and (Tn) is a universal sequence such ...
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Sequences of differential operators: exponentials, hypercyclicity and equicontinuity

Bernal González, Luis; Prado Tendero, José Antonio (Polish Academy of Sciences, Institute of Mathematics, 2001-01-01)
In this paper, an eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new ...
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Holomorphic T-monsters and strongly omnipresent operators

Bernal González, Luis; Calderón Moreno, María del Carmen (Elsevier, 2000-06-01)
Assume that G is a nonempty open subset of the complex plane and that T is an operator on the linear space of holomorphic ...
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A Seidel-Walsh theorem with linear differential operators

Bernal González, Luis; Calderón Moreno, María del Carmen (Springer, 1999-05-01)
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 ...
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Holomorphic functions having large images under the action of differential operators

Bernal González, Luis (Elsevier, 1999-02-15)
We prove in this note that, given a simply connected domain G in the complex plane and a sequence of infinite order linear ...
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Hypercyclic sequences of differential and antidifferential operators

Bernal González, Luis (Elsevier, 1999-02-01)
In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space ...
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On universal entire functions with zero-free derivatives

Bernal González, Luis (Springer, 1997-04-01)
We prove in this note a generalization of a theorem due to G. Herzog on zero-free universal entire functions. Specifically, ...
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Small entire functions with extremely fast growth

Bernal González, Luis (Elsevier, 1997-03-15)
We prove in this note that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is ...
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A lot of “counterexamples” to Liouville's theorem

Bernal González, Luis (Elsevier, 1996-08-01)
We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M ...
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Universal functions for taylor shifts

Bernal González, Luis (Taylor & Francis, 1996-01-01)
In this paper a new sort of operators, the Taylor shifts, is introduced. They appear as a generalization of weighted ...
PhD Thesis
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Funciones universales para operadores de composición en superficies de Riemann

Bernal González, Luis; Montes Rodríguez, Alfonso (1994-01-01)
"Esta memoria está dividida en cuatro capítulos. En el Capítulo cero de preliminares introducimos la notación y recordamos ...
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Orden relativo de crecimiento de funciones enteras

Bernal González, Luis (Universitat de Barcelona, 1988-01-01)
In this paper, we essay a generalization of the classical concept of growth order of an entire function. We define the new ...
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Exponente de convergencia generalizado de una sucesión compleja

Bernal González, Luis (Universitat de Barcelona, 1987-01-01)
Our aim in this paper is to give several new expressions for the kth-convergence exponent of a complex sequence, and an extension of this concept to a certain class of real functions.
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Funciones con derivadas sucesivas grandes y pequeñas por doquier

Bernal González, Luis (Universitat de Barcelona, 1987-01-01)
In this paper we show that, given two double sequences of positive real numbers, α and β, the subset of all functions ...
PhD Thesis