Multidimensional Borg-Levinson Theorem
Analysis of PDEs
2009-11-10 v1 Mathematical Physics
math.MP
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 and the eigenvalues corresponding to a set of impedances in the Robin boundary condition which vary on . 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.
Cite
@article{arxiv.math/0406582,
title = {Multidimensional Borg-Levinson Theorem},
author = {Yaroslav Kurylev and Matti Lassas and Ricardo Weder},
journal= {arXiv preprint arXiv:math/0406582},
year = {2009}
}