Discrete Entailment-Based Linking and -EE Nouns in English

Barker (1998) argues that since the referent of an -ee noun can be an indirect object, a direct object, a prepositional object, or a subject, -ee nouns cannot be described as a syntactic natural class. Portero Muñoz (2003) concurs and offers a semantic analysis based on Logical Structure (LS) in the framework of Role and Reference Grammar (RRG). This article proposes that RRG's macroroles (Actor and Undergoer) can be derived with two entailments and without any need for LS. Its analysis improves Portero Muñoz's, presenting additional evidence that subjects that allow -ee noun formation are Undergoers. It also explains why most -ee nouns are direct objects in spite of the fact that the suffix originated as a referent for indirect objects. Finally, it offers an explanation for nouns like amputee, pluckee, twistee, benefactee, malefactee, biographee, catapultee, razee, standee, attendee

Holomorphic functions having large images under the action of differential operators

We prove in this note that, given a simply connected domain G in the complex plane and a sequence of infinite order linear differential operators generated by entire functions of subexponential type satisfying suitable conditions, then there are holomorphic functions f on G such that the image of any open subset under the action of those operators on f is arbitrarily large. This generalizes an earlier result about images of derivatives. A known statement about close orbits is also strengthened.Dirección General de Enseñanza Superior (DGES). Españ

Linear Kierst-Szpilrajn theorems

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 exist a dense linear manifold and a closed infinite-dimensional linear manifold of holomorphic functions in D whose domain of holomorphy is D except for the null function. The existence of a dense linear manifold of noncontinuable functions is also shown in any domain for its full space of holomorphic functions.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). Españ

Backward Φ-shifts and universality

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 properties of the underlying selfmappings. Applications to hypercyclicity theory are given. In particular, Rolewicz’s theorem on hypercyclicity of scalar multiples of the classical backward shift is extended.Plan Andaluz de Investigación (Junta de Andalucía

Hypercyclic subspaces in Fréchet spaces

In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes earlier work of several authors.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). Españ

Compositionally universal entire functions on the plane and the punctured plane

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 that only for translations and rotation-dilations there can be entire functions whose orbits present universality. Boundedness of these functions on unbounded sets as well as frequent universality on the whole plane are also analyzed.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e InnovaciónMinisterio de Ciencia y Tecnología (MCYT). Españ

Universal entire functions for affine endomorphisms of C N

In this paper the affine endomorphisms of C N which support compositionally universal entire functions are completely characterized.Plan Andaluz de Investigación (Junta de Andalucía

Small entire functions with extremely fast growth

We prove in this note 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 such that limz→∞ exp(|z|α)f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, the growth index of each nonnull function of M is infinite with respect to any prefixed sequence of nonconstant entire functions.Dirección General de Investigación Científica y Técnica (DGICYT). Españ

Interpolation by hypercyclic functions for differential operators

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 of holomorphic functions on Ω. The orbit is taken with respect to any fixed non-scalar differential operator generated by an entire function of subexponential type, thereby extending a recent result about MacLane-hypercyclicity due to Costakis, Vlachou and Niess.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Educación y Ciencia (MEC). Españ