A continuous frame representation for an abstract shearlet group

Abstract

Let \({\mathbb {S}}\) be a locally compact abstract shearlet group and \(\sigma :{\mathbb {S}}\rightarrow {\mathcal {U}}({\mathcal {H}})\) be a representation of \({\mathbb {S}}\) on a separable Hilbert space \({\mathcal {H}}\). We give a necessary and sufficient condition for the family of representation coefficients to be a continuous shearlet frame. Furthermore relations between continuous shearlet frames associated to a given representation and its irreducible sub-representations are investigated.