Abstract:

Wavelet systems are generated by translation and dilation $\frac{1}{\sqrt{a}}f(x/a-b/a)$ where $a>0$. In some situations the dilation by $a$ can be replaced by the action of a larger group, and we will investigate the case when case when this group is the automorphism group of a symmetric cone. We will show that the Besov spaces on symmetric cones, defined by Bekolle, Bonami, Garrigos and Ricci via a Littlewood-Paley decomposition of the cone, can be described by wavelets. In particular we give a wavelet characterization via the quasi-regular representation of the semi-direct product of the automorphism group on the cone and the ambient vector space.