Homogeneous spaces and square-integrable representations

Abstract

For a locally compact group $G$ and a compact subgroup $H$ of $G$, the square-integrable representations of group $G$ and homogeneous space $G/H$ are described. Also, the connection between the existence of admissible wavelets for locally compact groups and their homogeneous spaces is compared. Moreover, some properties of admissible wavelets and wavelet constants for homogeneous space $G/H$ are investigated, when $G$ is unimodular.