Peter-Weyl Theorem for Homogeneous Spaces of Compact Groups

Abstract

This paper presents a structured formalism for a constructive generalization of the Peter-Weyl Theorem over homogeneous spaces of compact groups. Let H be a closed subgroup of a compact group G and µ be the normalized G-invariant measure on the compact left coset space G/H. We then present an abstract T H -version of the Peter-Weyl Theorem for the Hilbert function space L2 (G/H,µ).