The square integrable representation of Homogeneous space associated to semi-direct product group

Document Type: Research Paper




In this paper, we introduce the square-integrable representations of homogeneous space with respect to relatively invariant measures. Moreover, we investigate the necessary and sufficient condition for the square-integrable representation of a semi-direct product group and the homogeneous space associated with this group. Furthermore,  we explain the relationship between the admissible wavelets on the semi-direct product group and on its homogeneous space.