SOME RESULTS ON INVERSE SCATTERING

Abstract

A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with “incomplete” data, (4) Inverse scattering for inhomogeneous Schrödinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand–Levitan, Marchenko, and Krein inversion methods, (7) The Newton–Sabatier and Cox–Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, 9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties.