Abstract Coherent State Transforms Over Homogeneous Spaces of Compact Groups

This paper presents theoretical aspects of a unified generalization for the abstract theory of coherent state/voice transforms over homogeneous spaces of compact groups using operator theory. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μμ be the normalized G-invariant measure on G/H associated to the Weil’s formula with respect to the probability measures of G, H. Let (π,Hπ)(π,Hπ) be a continuous unitary representation of G with non-zero mean over H. In this article, we introduce the generalized notion of coherent state/voice transform associated to ππ on the Hilbert function L2(G/H,μ)L2(G/H,μ). We then study basic analytic properties of these transforms.