Multidimensional Borg-Levinson inverse spectral problems
Résumé
This text deals with multidimensional Borg-Levinson inverse theory. Its main purpose is to establish that the Dirichlet eigenvalues and Neumann boundary data of the operator −∆+q, acting in a bounded domain of R d with d 2, uniquely determine the realvalued bounded potential q. We first address the case of incomplete spectral data, where finitely many boundary spectral eigen-pairs remain unknown. Under suitable summability condition on the Neumann data, we also consider the case where only the asymptotic behavior of the eigenvalues is known. Finally, we use the multidimensional Borg-Levinson theory for solving parabolic inverse coefficient problems.
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