Resonance free domains for non globally analytic potentials

We study the resonances of the semiclassical Schrodinger operator P = - h(2) Delta + V near a non-trapping energy level lambda(0) in the case when the potential V is not necessarily analytic on all of R-n but only outside some compact set. Then we prove that for some delta > 0 and for any C > 0, P admits no resonance in the domain I Omega = [lambda(0)-delta, lambda(0)+delta]-i[0, Ch log (h(-1))] if V is C-infinity, and Omega = [lambda(0) - delta, lambda(0) + delta]-i[0, deltah(1-1/s)] if V is Gevrey with index s. Here delta > 0 does not depend on It and the results are uniform with respect to h > 0 small enough.