Harmonic analysis on SU$(n,n)/ SL(n,{\Bbb C})\times {\Bbb R}_+^*$.

Abstract: We find an explicit expression for the spherical functions on the ordered symmetric space ${\cal M=SU(n,n)/SL(n,{\Bbb C})\times {\Bbb R}^*_+}$, we formulate and prove a Paley-Wiener theorem for the spherical Laplace transform on ${\cal M}$ and we find an inversion formula for the Abel transform on ${\cal M}$.

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