Multi-dimensional inverse boundary problems by BC-method: Groups of transformations and uniqueness results

Abstract

We consider inverse spectral boundary value problems for a general self-adjoint elliptic operator of the second order with real coefficients and describe the group of transformations preserving the boundary spectral data. In particular, we describe the groups of admissible transformations for the anisotropic conductivity operator and general isotropic one in a domain of Euclidean space. For the Schrödinger operator on a Riemannian manifold we prove the uniqueness result and provide a procedure for the reconstruction of the manifold (with metrics) and the potential in terms of the boundary spectral data. All results are obtained for operators controllable from the boundary.