THE MULTIDIMENSIONAL GELFAND INVERSE PROBLEM FOR NONSELF-ADJOINT OPERATORS

This paper is devoted to the Gel'fand inverse problem for the pair (M, A) where M is a compact manifold with boundary and A is a second-orde r elliptic operator on M. It is shown that (under some requirements of the geometric character) the boundary spectral data determine M uniqu ely and A to within the group of the generalized gauge transformations . Applications to the inverse boundary problem in a bounded domain in R-n, n greater than or equal to 1, are also considered.