Resonances for steplike potentials: forward and inverse results

Abstract. We consider resonances associated to the one-dimensional Schrödinger operator − d2 dx2 + V (x), where V (x) = V+ if x> xM and V (x) = V − if x < −xM, with V+ 6 = V−. We obtain asymptotics of the resonance-counting function for several regions. Moreover, we show that in several situations, the resonances, V+, and V − determine V uniquely up to translation