MULTIDIMENSIONAL INVERSE BOUNDARY-PROBLEMS BY BC-METHOD - GROUPS OF TRANSFORMATIONS AND UNIQUENESS RESULTS

We consider inverse spectral boundary value problems for a general sel f-adjoint elliptic operator of the second order with real coefficients and describe the group of transformations preserving the boundary spe ctral data. In particular, we describe the groups of admissible transf ormations for the anisotropic conductivity operator and general isotro pic one in a domain of Euclidean space. For the Schrodinger operator o n a Riemannian manifold we prove the uniqueness result and provide a p rocedure for the reconstruction of the manifold (with metrics) and the potential in terms of the boundary spectral data. All results are obt ained for operators controllable from the boundary.