Supercyclic and hypercyclic non-convolution operators

A continuous linear operator T : X -> X is hypercyclic/supercyclic if there is a vector f is an element of X such that the orbit Orb (T, f) = {T(n)f}/respectively the set of scalar-multiples of the orbit elements, forms a dense set. A famous theorem, due to G. Godefroy & J. Shapiro, states that every non-scalar convolution operator, on the space H of entire functions in d variables, is hypercyclic (and thus supercyclic). This motivates us to study cyclicity of operators on H outside the set of convolution operators. We establish large classes of supercyclic and hypercyclic non-convolution operators.