The indefinite orthogonal group O(p+1,q+1) acts as the Moebius group of conformal transformations on Rp+q, and preserves the space of solutions of the ultrahyperbolic Laplace equation on Rp+q.Inspired by the idea of Sato's hyperfunctions, we construct in an intrinsic and natural way a Hilbert space of solutions by the integration of the data of solutions over a hypersurface, and give a new construction of its minimal unitary representation for p+q even.
© Toshiyuki Kobayashi