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Spherical functions on ordered symmetric spaces

Jacques FarautJoachim HilgertGestur Ólafsson — 1994

Annales de l'institut Fourier

We define on an ordered semi simple symmetric space = G / H a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when G is a complex group, H a real form of G , and when ...

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