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

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