Multi-dimensional inverse scattering theory (Q2749821)

The author presents an original point of view and some interesting developments on the Faddeev's theory concerning the multi-dimensional inverse problem of scattering. The aim of this article is to give a brief survey on the following subjects:NEWLINENEWLINENEWLINE1. What is the direction-dependent Green operator, the central idea of Faddeev?NEWLINENEWLINENEWLINE2. To what extent can one understand the inverse problem by Faddeev's theory?NEWLINENEWLINENEWLINE3. New developments (including author's research).NEWLINENEWLINENEWLINEEssentially the Schrödinger operator is exemplified, but also some applications to the wave equation in stratified medium and Dirac equations are given.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].