Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction

An analysis of a Green’s function approach (based on wave splitting) to the one-dimensional electromagnetic inverse problem is given. The Green’s functions refer to split components of the fundamental solution. The linear system of equations for the Green’s functions is shown to be well-posed for the inverse problem and stability estimates, theorems on existence, uniqueness, local correctness, and convergence are given.