Hypercyclic sequences of PDE-preserving operators

A sequence T=(Tn) of continuous linear operators Tn:X→X is said to be hypercyclic if there exists a vector x∈X, called hypercyclic for T, such that {Tnx:n⩾0} is dense. A continuous linear operator, acting on some suitable function space, is PDE-preserving for a given set of convolution operators, when it map every kernel set for these operators invariantly. We establish hypercyclic sequences of PDE-preserving operators on H(Cd), and study closed infinite-dimensional subspaces of, except for zero, hypercyclic vectors for these sequences.