The bounded spherical functions on the Cartan Motion group and Generalizations for the eigenspaces of the Laplacian on Rn

The bounded spherical functions are determined for a real Cartan Motion group which is a generalization for the case when the Cartan Motion group is complex written by Helgason Sigurdur . Also, I will do a further step of the Laplacian on R n . I consider the case when K is transitive on the spheres about 0 in Rn ,n > 1