Hypercyclic subspaces for sequences of finite order differential operators

Abstract

It is proved that, if $\left(P_n\right)$ 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, as well a dense $c$-dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence $\left(P_n\right(D\left)\right)$ of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercyclic function.