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

Salem Ben Said (1)

1 IECN - Institut Élie Cartan de Nancy

Let $\q$ 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.

Domaines: Analyse fonctionnelle [math.FA]

Salem Ben Said. A Paley-Wiener theorem for the Bessel-Laplace transform (I): The case $SU(n,n)/GL(n,C)_+$. 2006. ⟨hal-00095335⟩