Related papers: Common hypercyclic functions for translation opera…
We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.
We prove the existence of common hypercyclic, entire functions for certain families of translation operators.
We show that families of translation operators, where the translates grow exponentially fast, do not admit common hypercyclic functions. The result is close to be optimal.
It is well known that there are entire functions whose orbit approximates any other entire function under the action of a sequence of translation operators . This result also holds for an uncountable family of sequences of translation…
Let X,Y be two separable Banach or Frechet spaces , and (Tn) , n=1,2,... be a sequence from linear and continuous operators from X to Y . We say that the sequence (Tn) , n=1,2,... is universal , if there exists some vector v in X such that…
We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic…
We prove the existence of entire functions that achieve universal approximations on certain countable sequences of translation operators .
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
We show that the non-zero multiples of the derivative operator and the non-zero multiples of non-trivial translation operators on the space of entire functions share a common hypercyclic subspace, i.e. a closed infinite-dimensional subspace…
We study the existence of a common hypercyclic vector for different families of composition operators.
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…
In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given…
In this paper, we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context of locally compact hypergroups.
It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions,…
We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an…
Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for…
We investigate the existence of a common hypercyclic vector for a family $(T_\lambda)_{\lambda\in \Lambda}$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of…
A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a…