Representation of semigroups in rigged Hilbert spaces: Subsemigroups of the Weyl–Heisenberg group

In this paper we study how differentiable representations of certain subsemigroups of the Weyl–Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl–Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are also investigated within the context of the results developed here.