Intertwining operators in inverse scattering

In these notes we are going to present a technique which is a multi-dimensional analogue of some methods which are nowadays standard inscattering theory on the real line for the Schrödinger operator. These methods are based on the construction of operators intertwining the Schrödinger operator with the free operator, obtained when the potential term is removed. The multi-dimensional technique using intertwining operators as a tool for the study of Schrödinger operators has its origin in a famous paper by L. D. Faddeev. Various extensions of this technique have been developed during the last years by the second author of this article