A Paley-Wiener theorem for the Bessel-Laplace transform (I): The case $SU(n,n)/GL(n,C)_+$

Abstract

Soumis à Journal of Lie theoryLet \q be the tangent space to the noncompact causal symmetric space SU(n,n)/SL(n,\C)\times \R^*_+ at the origin. In this paper we give an explicit formula for the Bessel functions on \q, and we then use it to prove a Paley-Wiener theorem for the Bessel-Laplace transform on \q. Further, an Abel transform for \q is defined and inverted