Compositional frequent hypercyclicity on weighted Dirichlet spaces

Abstract

It is proved that, in most cases, a scalar multiple of a linear-fractional generated composition operator λCϕ acting on a weighted Dirichlet space Sν of holomorphic functions in the open unit disk is frequently hypercyclic if and only if it is hypercyclic. In fact, this holds for all triples (ν, λ, ϕ) with the possible exception of those satisfying ν ∈ [1/4, 1/2), |λ| = 1, ϕ = a parabolic automorphism.