Stability of the inversion of 3D fixed-frequency scattering data (Q1209497)

The author considers scattering solutions associated with the solution of the differential equation \([\nabla^ 2+k^ 2-q(x)]u=0\) where \(q(x)\) is small for large \(| x|\). He gives exact inversion formulae and points out that they involve the inversion of a very ill-conditioned infinite matrix. He then discusses the stability of the results and gives an example. He closes with the formulation of a number of open problems. This paper is a report of an invited lecture and of the 32 references, 29 are by the author.