On the wave operator for dissipative potentials with small imaginary part

Abstract

We determine the range of the incoming wave operator for the pair of operators (−Δ,−Δ+V₁(x)−iεV₂(x)) on L²(Rⁿ) under the conditions n≥3 and 0 is a regular point of −Δ+V₁, V₂≥0 and ε>0 is small enough. This implies that the dissipative scattering operator is bijective.