This paper presents the abstract notion of Poisson summation formulas for
homogeneous spaces of compact groups. Let G be a compact group, H be a closed
subgroup of G, and μ be the normalized G-invariant measure over the left coset space
G/H associated to the Weil’s formula. We prove that the abstract Fourier transform
over G/H satisfies a generalized version of the Poisson summation formula.