Multidimensional Borg-Levinson Theorem

Details Multidimensional Borg-Levinson Theorem Multidimensional Borg-Levinson Theorem

2004-06-28

arxiv.org/abs/math/0406582v1

Inverse Problems vol 21 (2005) 1685-1696

Mathematics

Analysis of PDEs

Scientific paper

10.1088/0266-5611/21/5/011

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.

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