The spherical Bochner theorem on semisimple Lie groups
Let G be a connected semisimple Lie group with finite center and K a maximal compact subgroup. Denote (i) Harish-Chandra's Schwartz spaces by Cp(G)(0
Barker, William H., "The spherical Bochner theorem on semisimple Lie groups" (1975). Mathematics Faculty Publications. 4.