  We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n,R)
and H = S(GL(n-1,R) x GL(1,R)). We classify all minimal parabolic subgroups of
G for which the associated cuspidal integrals are convergent and discuss the
possible definitions of cusp forms. Finally, we show that the closure of the
direct sum of the discrete series of representations of G/H coincides with the
space of cusp forms.
