Abstract Poisson summation formulas over homogeneous spaces of compact groups (Q1683630)

Let \(G\) be a compact group and \(H\) be a closed subgroup of \(G\). The author studies some abstract aspects of harmonic analysis on Banach function spaces over the compact homogeneous space \(G/H\). He introduces the abstract notion of dual space \(\widehat{G/H}\) for the homogeneous space \(G/H\) and presents the theoretical definition of the abstract operator-valued Fourier transform over the compact homogeneous space \(G/H\). He also proves that the abstract Fourier transform over \(G/H\) satisfies a generalized version of the Poisson summation formula.