Determination of the Schrödinger-Robin operator by incomplete or asymptotic spectral boundary data

Abstract: This article deals with the inverse problem of determining the unbounded real-valued electric potential of the Robin Laplacian on a bounded domain of dimension 3 or greater, by incomplete knowledge of its boundary spectral data. Namely, the main result establishes that the unknown potential can be H\"older stably retrieved from the asymptotic behavior of the eigenvalues and the sequence of the boundary measurements of the corresponding eigenfunctions where finitely many terms are missing.