2,712 research outputs found
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
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
Linear structure of the weighted holomorphic non-extendibility
In this paper, it is proved that, for any domain G of the complex plane, there exist an infinite-dimensional closed linear submanifold M1 and
a dense linear submanifold M2 with maximal algebraic dimension in the space H(G) of holomorphic functions on G such that G is the
domain of holomorphy of every nonzero member of f of M1 or M2 and, in addition, the growth of f near each boundary point is as fast
as prescribed.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). Españ
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
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
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
Algebraic genericity of strict-order integrability
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 < p) contains, except for zero, large subspaces of
Lp (µ, X). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many nonintegrable functions of order q can be obtained even on any nonempty open subset of X, assuming that X is a topological space and µ is a Borel measure on X satisfying appropriate properties.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e InnovaciónMinisterio de Ciencia y Tecnología (MCYT). Españ
Common hypercyclic functions for multiples of convolution and non-convolution operators
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 than 1/2. The same result holds if T is a finite-order linear differential operator with non-constant coefficients.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Educación y Ciencia (MEC). Españ
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