Wave Front Sets and Singular Supports of Convolutions.
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
The paper gives a new application of the white noise distribution theory via a proof of irreducibility of the energy representation of a group of -maps from a compact Riemann manifold to a semi-simple compact Lie group.