Multidimensionnel Borg-Levinson uniqueness and stability results for the Robin Laplacian with unbounded potential

TL;DR

This paper investigates the uniqueness and stability in reconstructing unbounded potentials of Schrödinger operators with Robin boundary conditions from spectral boundary data in higher-dimensional domains.

Contribution

It provides new multidimensional results on the inverse spectral problem for Schrödinger operators with unbounded potentials and Robin boundary conditions.

Findings

Establishes uniqueness of potential recovery from spectral data.

Proves stability estimates for the inverse problem.

Extends results to unbounded potentials in higher dimensions.

Abstract

This article deals with the uniqueness and stability issues in the inverse problem of determining the unbounded potential of the Schr\"odinger operator in a bounded domain of dimension 3 or greater, endowed with Robin boundary condition, from knowledge of its boundary spectral data. These data are defined by the pairs formed by the eigenvalues and either full or partial Dirichlet measurement of the eigenfunctions on the boundary of the domain.