Harmonic analysis on the one-sheet hyperboloid and multiperipheral inclusive distributions

The harmonic analysis of the n particle inclusive distributions and the partial diagonalization of the ABFST multiperipheral integral equation at vanishing momentum transfer are treated rigorously on the basis of the harmonic analysis of distributions defined on the one- sheet hyperboloid in four dimensions. A complete and consistent treatment is given of the Radon and Fourier transforms on the hyperboloid and of the diagonalization of invariant kernels. The final result is a special form of the O(3, 1) expansion of the inclusive distributions, which exhibits peculiar dynamical features, in particular fixed poles at the nonsense points, which are essential in order to get the experimentally observed behaviour. (32 refs).