Hypercyclic and chaotic convolution operators

Every convolution operator on a space of ultradifferentiable functions of B eurling or Roumieu type and on the corresponding space of ultradistribution s is hypercyclic and chaotic when it is not a multiple of the identity. The operator of differentiation is hypercyclic on the space A(-infinity), but it need not be hypercyclic on radial weighted algebras of entire functions.