The Θ-spherical transform and its inversion - Pasquale, Angela (MATHEMATICA SCANDINAVICA, 2004)
The Θ-spherical transform is defined as a simultaneous generalization of the Harish-Chandra’s spherical transform on Riemannian symmetric spaces of noncompact type and of the spherical Laplace transform on noncompactly causal symmetric spaces as defined by Faraut, Hilgert and Ólafsson. An extension of Ólafsson’s expansion formula allows us to deduce an inversion formula for the Θ-spherical transform on the space of W_Θ-invariant C^∞ functions with compact support.