Operator integral in multidimensional spectral Inverse Problem

An approach to the Inverse Problems based upon the Boundary Control Theory (BC-method; M. Belishev, 1986) is developed. Working effectively in the Inverse Problems, M. Brodskii's operator integral is introduced. It has a dynamical nature connected with a propogation of discontinuities of the wave fields. Operator integral is applied to solve the problem of recovering of a potential in the Schrödinger operator on a Riemannian manifold via its spectral data. Bibliography: 27 titles.