  In the previous paper [25], Stolarsky's invariance principle, known for point
distributions on the Euclidean spheres [27], has been extended to the real,
complex, and quaternionic projective spaces and the octonionic projective
plane. Geometric features of these spaces as well as their models in terms of
Jordan algebras have been used very essentially in the proof. In the present
paper, we give a new pure analytic proof of the extended Stolarsky's invariance
principle, relying on the theory of spherical functions on compact symmetric
Riemannian manifolds of rank one.
