Determination of the Schr\"odinger-Robin operator by incomplete or asymptotic spectral boundary data

TL;DR

This paper investigates how to stably recover an electric potential in a Robin Laplacian from incomplete boundary spectral data, including asymptotic eigenvalues and boundary measurements, even with missing data.

Contribution

It introduces a method to determine the potential using incomplete spectral data with asymptotic information, advancing inverse spectral problem techniques.

Findings

Potential can be stably reconstructed from asymptotic eigenvalues.

Boundary measurements of eigenfunctions enable potential recovery.

The method handles missing spectral data effectively.

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.