Journal of Lie Theory, Vol. 10, No. 2, pp. 311-322 (2000)

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

Nils Byrial Andersen and Jérémie M. Unterberger

Nils Byrial Andersen
Department of Mathematics
Louisiana State University
Baton Rouge
LA 70803
Jérémie M. Unterberger
Dipartimento di Matematica
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 TORINO

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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