Resonances for steplike potentials: forward and inverse results

الأصل · EN

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