Conformally Invariant Hilbert Structure on the Solution Space of the Ultrahyperbolic Laplace Equation on R^p+q,
Tsukuba Conference on Integral Geometry and Harmonic Analysis (organized by Fulton Gonzalez, Tomoyuki Kakehi and Toshio Oshima), University of Tsukuba, Japan, 7-10 August 2006.

The indefinite orthogonal group O(p+1,q+1) acts as the Moebius group of conformal transformations on R^p+q, and preserves the space of solutions of the ultrahyperbolic Laplace equation on R^p+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