Spherical functions on mixed symmetric spaces

In this article we compute the spherical functions which are associated to hyperbolically ordered symmetric spaces H\G. These spaces are usually not semisimple; one prominent example is given by H\G = (ℝn ⋊ Gl(n; ℝ))n(Hn⋊Sp(n; ℝ)) with Hn the (2n+1)-dimensional Heisenberg group. © 2001 American Mathematical Society