*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