Partial Poisson transforms on SU( n, n) / SL(n, C) x R+*.

In this article, we introduce a partial Poisson transform on the affine symmetric space SU(n, n) / SL(n, C) x R+* and prove that this transform is a continuous SU(n, n)-homomorphism. We also give the form for the Fourier transform of the Poisson kernel. [ABSTRACT FROM AUTHOR]