Wavelet transforms via generalized quasi-regular representations

The construction of the well-known continuous wavelet transform has been extended before to higher dimensions. Then it was generalized to a group which is topologically isomorphic to a homogeneous space of the semidirect product of an abelian locally compact group and a locally compact group. In this paper, we consider a more general case. We introduce a class of continuous wavelet transforms obtained from the generalized quasi-regular representations. To define such a representation of a group G, we need a homogeneous space with a relatively invariant Radon measure and a character of G.