Now showing items 1-20 of 81

    • Icon

      A lot of “counterexamples” to Liouville's theorem  [Article]

      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 is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any ...
    • Icon

      A Seidel-Walsh theorem with linear differential operators  [Article]

      Bernal González, Luis; Calderón Moreno, María del Carmen (Springer, 1999-05)
      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 ...
    • Icon

      Algebraic genericity of strict-order 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 < ...
    • Icon

      Backward Φ-shifts and universality  [Article]

      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 shifts associated to certain selfmappings of E. We characterize their universality in terms of dynamical ...
    • Icon

      Banach spaces of universal Taylor series in the disc algebra  [Article]

      Bernal González, Luis; Jung, Andreas; Müller, Jürgen (Springer, 2016-09)
      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 ...
    • Icon

      Boundary-chaotic behaviour of continuous functions under the action of operators  [Article]

      Bernal González, Luis; Calderón Moreno, María del Carmen (Cambridge University Press, 2003-06)
      In this paper we introduce two classes of operators on spaces of continuous functions with values in F-spaces under the action of which many functions behave chaotically near the boundary. Several examples, including ...
    • Icon

      Boundary-nonregular functions in the disc algebra and in holomorphic Lipschitz spaces  [Article]

      Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; López-Salazar Codes, Jerónimo; Seoane Sepúlveda, Juan Benigno (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 ...
    • Icon

      Common hypercyclic functions for multiples of convolution and non-convolution operators  [Article]

      Bernal González, Luis (American Mathematical Society, 2009-11)
      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 ...
    • Icon

      Compositional frequent hypercyclicity on weighted Dirichlet spaces  [Article]

      Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (The Belgian Mathematical Society, 2010-02)
      It is proved that, in most cases, a scalar multiple of a linear-fractional generated composition operator λCϕ acting on a weighted Dirichlet space Sν of holomorphic functions in the open unit disk is frequently hypercyclic ...
    • Icon

      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– ...
    • Icon

      Compositional universality in the N-dimensional ball  [Article]

      Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo; Calderón Moreno, María del Carmen (De Gruyter, 2007-05)
      It is proved in this note that a sequence of automorphisms on the N-dimensional unit ball acts properly discontinuously if and only if its corresponding sequence of composition operators is universal on the Hardy space of ...
    • Icon

      Compositionally universal entire functions on the plane and the punctured plane  [Article]

      Bernal González, Luis (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 ...
    • Icon
    • Icon

      Cyclicity of coefficient multipliers: Linear structure  [Article]

      Bernal González, Luis; Calderón Moreno, María del Carmen; Prado Bassas, José Antonio (Springer, 2007-03)
      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 ...
    • Icon

      Dense linear manifolds of monsters  [Article]

      Bernal González, Luis; Calderón Moreno, María del Carmen (Elsevier, 2002-12)
      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 ...
    • Icon

      Dense-lineability of sets of Birkhoff-universal functions with rapid decay  [Article]

      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 increasing positive function on the positive real numbers. We prove the existence of a dense linear ...
    • Icon

      Existence and nonexistence of hypercyclic semigroups  [Article]

      Bernal González, Luis; Grosse-Erdmann, Karl-Goswin (American Mathematical Society, 2007-03)
      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– ...
    • Icon

      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 kth-convergence exponent of a complex sequence, and an extension of this concept to a certain class of real functions.
    • Icon

      Exponential type of hypercyclic entire functions  [Article]

      Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 2002-04)
      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 ...
    • Icon

      Families of strongly annular functions: linear structure  [Article]

      Bernal González, Luis; Bonilla Ramírez, Antonio Lorenzo (Springer, 2013-01)
      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 ...