Inverse spectral problem for delta potentials

The scattering problem for the linear Schrödinger equation on the entire axis has been considered. Conditions under which the knowledge of the discrete spectrum of the Schrödinger operator is sufficient for the reconstruction of the potential have been determined. The main difference from the soliton sector is the self-similarity of the problem under consideration with respect to the extension of the spectral parameter $\lambda$. This makes it possible to reduce the inverse scattering problem to the study of the singularity of the Green's function at $\lambda = 0$.