Hypercyclic and Chaotic Convolution Operators

Every convolution operator on a space of ultradifferentiablefunctions of Beurling or Roumieu type and on the correspondingspace of ultradistributions is hypercyclic and chaotic whenit is not a multiple of the identity. The operator of differentiationis hypercyclic on the space A^–, but it need not be hypercyclicon radial weighted algebras of entire functions.