  Let $\Gamma$ be a Zariski dense Kleinian Schottky subgroup of PSL2(C). Let
$\Lambda(\Gamma)$ be its limit set, endowed with a Patterson-Sullivan measure
$\mu$ supported on $\Lambda(\Gamma)$. We show that the Fourier transform
$\widehat{\mu}(\xi)$ enjoys polynomial decay as $\vert \xi \vert$ goes to
infinity. This is a PSL2(C) version of the result of Bourgain-Dyatlov [8], and
uses the decay of exponential sums based on Bourgain-Gamburd sum-product
estimate on C. These bounds on exponential sums require a delicate
non-concentration hypothesis which is proved using some representation theory
and regularity estimates for stationary measures of certain random walks on
linear groups.
