A simple proof of a multidimensional Borg-Levinson type theorem

TL;DR

This paper presents a straightforward proof showing that spectral boundary data uniquely determine the potential in a multidimensional Schrödinger operator on certain Riemannian manifolds, extending to incomplete data cases.

Contribution

It offers a simplified proof of a multidimensional Borg-Levinson theorem and addresses the case of incomplete spectral boundary data.

Findings

Spectral boundary data uniquely determine the potential.

The proof applies to admissible Riemannian manifolds.

Extension to incomplete data cases is sketched.

Abstract

We provide a simple and short proof of a multidimensional Borg-Levinson type theorem. Precisely, we prove that the spectral boundary data determine uniquely the corresponding potential appearing in the Sch\"odinger operator on an admissible Riemannian manifold. We also sketch the proof of the case of incomplete spectral boundary data.