| Abstract: | An approach to inverse problems based upon boundary control theory (the BC-method; M. Belishev, 1986) is developed. M. Brodskii's operator integral is introduced, which works effectively in the inverse problems. It has dynamical nature connected with propagation of discontinuities of wave fields. The integral is proved to converge for (large) times when the geodesic normal field starting at the boundary loses its regularity. The operator integral is applied to solving the problem of recovering the potential in the Schrödinger operator on a Riemannian manifold from its spectral data. Bibliography: 27 titles. |
