Question of Uniqueness of Recovery of Potential by Spectrum in the Inverse Borg Levinson Problem with Robin Boundary Conditions

Abstract

The inverse Borg -- Levinson problem with Robin boundary conditions, such that conditions for the uniqueness of the recovery of potential by spectrum are formulated for it, is considered in the paper. A similar problem, but with the Dirichlet boundary conditions, is enough studied. It is well known that the uniqueness of the recovery of potential is independent on removing of a finite number of spectral data in the inverse Borg -- Levinson problem with Dirichlet boundary conditions. In the present paper we prove that the theorem, which was obtained for the Dirichlet boundary conditions, holds also for problem with Robin boundary conditions. To this end, we prove the theorems about the uniqueness of recovery of potential in the inverse Borg -- Levinson problem with the Robin boundary conditions. Also we answer the following question. Suppose we know the nature of the asymptotic expansion of its eigenvalues. When this problem has a unique solution? The method to create a mathematical model of the recovery of potential in the inverse Robin problem is presented on the basis of it.