An operator integral in the multidimensional spectral inverse problem
Copyright policy )An operator integral in the multidimensional spectral inverse problem
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 for inverse problems. It has a 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.
Schrödinger operator, BC-method, potential, boundary control theory, Riemannian manifold, geodesic normal field, Brodskii's operator integral, Hermitian and normal operators (spectral measures, functional calculus, etc.), Vector-valued measures and integration, wave fields
Schrödinger operator, BC-method, potential, boundary control theory, Riemannian manifold, geodesic normal field, Brodskii's operator integral, Hermitian and normal operators (spectral measures, functional calculus, etc.), Vector-valued measures and integration, wave fields
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