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Lineability and modes of convergence [Article]
(Springer, 202001)In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are ...

Newtonian fluid flow in a thin porous medium with nonhomogeneous slip boundary conditions [Article]
(American Institute of Mathematical Sciences, 201906)We consider the Stokes system in a thin porous medium Ωε of thickness ε which is perforated by periodically distributed solid cylinders of size ε. On the boundary of the cylinders we prescribe nonhomogeneous slip boundary ...

[S]linear and convex structures in function families [Article]
(Elsevier, 20191015)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, ...

Monsters in Hardy and Bergman spaces [Article]
(Taylor & Francis, 2002)A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In ...

Families of strongly annular functions: linear structure [Article]
(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 ...

Backward Φshifts and universality [Article]
(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 ...

Interpolation by hypercyclic functions for differential operators [Article]
(Elsevier, 200904)We prove that, given a sequence of points in a complex domain Ω without accumulation points, there are functions having prescribed values at the points of the sequence and, simultaneously, having dense orbit in the space ...

Hypercyclic sequences of differential and antidifferential operators [Article]
(Elsevier, 199902)In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space of entire functions of several complex variables. Specifically, we generalize in several directions ...

Universal transforms of the geometric series under generalized Riesz methods [Article]
(Springer, 200403)In this paper generalized Riesz methods (R, p, M) of summability are considered. We prove that, to each open set O ⊂ C with adequate topological properties and each sequence {Pn} ⊂ C tending to infinity, we can associate ...

Linear subsets of nonlinear sets in topological vector spaces [Article]
(American Mathematical Society, 201401)For the last decade there has been a generalized trend in Mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying ...

Uoperators [Article]
(Cambridge University Press, 200502)Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain ...

Algebraic genericity of strictorder integrability [Article]
(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 < ...

Linear KierstSzpilrajn theorems [Article]
(Polish Academy of Sciences, Institute of Mathematics, 2005)We prove in this paper the following result which extends in a somewhat ‘linear’ sense a theorem by Kierst and Szpilrajn and which holds on many ‘natural’ spaces of holomorphic functions in the open unit disk D: There ...

Dense linear manifolds of monsters [Article]
(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 ...

Nowhere hölderian functions and Pringsheim singular functions in the disc algebra [Article]
(Springer, 201904)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 αh¨olderian at any point of the ...

Boundarychaotic behaviour of continuous functions under the action of operators [Article]
(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 ...

Sequences of differential operators: exponentials, hypercyclicity and equicontinuity [Article]
(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 ...

Common hypercyclic functions for multiples of convolution and nonconvolution operators [Article]
(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 ...

Existence and nonexistence of hypercyclic semigroups [Article]
(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– ...

Hypercyclic subspaces in Fréchet spaces [Article]
(American Mathematical Society, 200607)In this note, we show that every infinitedimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinitedimensional closed subspace consisting, except for zero, of ...