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Browsing by Author "Bernal González, Luis"
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A lot of “counterexamples” to Liouville's theorem [Article]
Bernal González, Luis (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 is dense in the space of all entire functions and, in addition, limz→∞ exp(zα) f(j)(z) = 0 on any ...

A SeidelWalsh theorem with linear differential operators [Article]
Bernal González, Luis; Calderón Moreno, María del Carmen (Springer, 199905)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 operators with constant coefficients, both of them satisfying suitable conditions. We prove ...

Algebraic genericity of strictorder integrability [Article]
Bernal González, Luis (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 < ...

Backward Φshifts and universality [Article]
Bernal González, Luis (Elsevier, 20050601)In this paper we consider spaces of sequences which are valued in a topological space E and study generalized backward shifts associated to certain selfmappings of E. We characterize their universality in terms of dynamical ...

Banach spaces of universal Taylor series in the disc algebra [Article]
Bernal González, Luis; Jung, Andreas; Müller, Jürgen (Springer, 201609)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 ...

Boundarychaotic behaviour of continuous functions under the action of operators [Article]
Bernal González, Luis; Calderón Moreno, María del Carmen (Cambridge University Press, 200306)In this paper we introduce two classes of operators on spaces of continuous functions with values in Fspaces under the action of which many functions behave chaotically near the boundary. Several examples, including ...

Boundarynonregular functions in the disc algebra and in holomorphic Lipschitz spaces [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; LópezSalazar Codes, Jerónimo; Seoane Sepúlveda, Juan Benigno (Springer, 201806)We prove in this paper the existence of dense linear subspaces in the classical holomorphic Lipschitz spaces in the disc all of whose nonnull functions are nowhere differentiable at the boundary. Infinitely generated free ...

Common hypercyclic functions for multiples of convolution and nonconvolution operators [Article]
Bernal González, Luis (American Mathematical Society, 200911)We prove the existence of a residual set of entire functions, all of whose members are hypercyclic for every nonzero scalar multiple of T, where T is the differential operator associated to an entire function of order less ...

Compositional frequent hypercyclicity on weighted Dirichlet spaces [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (The Belgian Mathematical Society, 201002)It is proved that, in most cases, a scalar multiple of a linearfractional generated composition operator λCϕ acting on a weighted Dirichlet space Sν of holomorphic functions in the open unit disk is frequently hypercyclic ...

Compositional hypercyclicity equals supercyclicity [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (University of Houston, 2007)In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected domain strictly contained in the complex plane is hypercyclic –that is, possesses some dense orbit– ...

Compositional universality in the Ndimensional ball [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (De Gruyter, 200705)It is proved in this note that a sequence of automorphisms on the Ndimensional unit ball acts properly discontinuously if and only if its corresponding sequence of composition operators is universal on the Hardy space of ...

Compositionally universal entire functions on the plane and the punctured plane [Article]
Bernal González, Luis (Springer, 201306)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 ...

Crecimiento relativo de funciones enteras. Aportaciones al estudio de las funciones enteras con índice exponencial finito [PhD Thesis]
Bernal González, Luis (19840929) 
Cyclicity of coefficient multipliers: Linear structure [Article]
Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Springer, 200703)In this paper we characterize various kinds of cyclicity of sequences of coefficient multipliers, which are operators defined on spaces of holomorphic functions. In the case of a single coefficient multiplier we characterize ...

Dense linear manifolds of monsters [Article]
Bernal González, Luis; Calderón Moreno, María del Carmen (Elsevier, 200212)In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic functions of a domain in the complex plane. The concept is more restrictive than that of ...

Denselineability of sets of Birkhoffuniversal functions with rapid decay [Article]
Bernal González, Luis; Calderón Moreno, María del Carmen; Luh, Wolfgang (Elsevier, 20100301)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 ...

Existence and nonexistence of hypercyclic semigroups [Article]
Bernal González, Luis; GrosseErdmann, KarlGoswin (American Mathematical Society, 200703)In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from –and considerably shorter than– ...

Exponente de convergencia generalizado de una sucesión compleja [Article]
Bernal González, Luis (Universitat de Barcelona, 1987)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.

Exponential type of hypercyclic entire functions [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 200204)In this paper the exponential type of hypercyclic entire functions with respect to a sequence (Φn(D)) of differential operators is considered, where every Φn is an entire function of exponential type. We prove that under ...

Families of strongly annular functions: linear structure [Article]
Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 201301)A function f holomorphic in the unit disk D is called strongly annular if there exists a sequence of concentric circles in D expanding out to the unit circle such that f goes to infinity as z goes to 1 through these ...