RESOLVENT APPROACH FOR 2-DIMENSIONAL SCATTERING PROBLEMS - APPLICATION TO THE NONSTATIONARY SCHRODINGER-PROBLEM AND THE KPI EQUATION

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An a nalog of the known Hilbert identity is derived. We demonstrate the rol e of this identity in the study of two-dimensional scattering. Conside ring the nonstationary Schrodinger equation as an example, we show tha t all types of solutions of the linear problem, as well as spectral da ta known in the literature, are given as specific values of this uniqu e function - the resolvent function. A new form of the inverse problem is formulated.