Yaroslav Kurylev, Matti Lassas and Ricardo Weder
Multidimensional Borg Levinson Theorem
(43K, AMSLATEX)
ABSTRACT. We consider the inverse problem of the reconstruction of a Schr\"odinger operator on a unknown
Riemannian manifold or a domain of Euclidean space. The data used
is a part of the boundary $\Gamma$ and the eigenvalues
corresponding to a set of impedances in the Robin boundary
condition which vary on $\Gamma$. The proof is based on the
analysis of the behaviour of the eigenfunctions on the boundary as
well as in perturbation theory of eigenvalues. This reduces the
problem to an inverse boundary spectral problem solved by the
boundary control method.