A quantitative Borg-Levinson theorem for a large class of unbounded potentials

TL;DR

This paper establishes a quantitative Borg-Levinson theorem applicable to a broad class of unbounded potentials, providing detailed proofs for higher dimensions and outlining extensions to lower dimensions and anisotropic cases.

Contribution

It introduces a new quantitative version of the Borg-Levinson theorem for unbounded potentials, including detailed proofs and extensions to various cases.

Findings

Proves a quantitative Borg-Levinson theorem for unbounded potentials in dimension ≥5.

Provides modifications for lower-dimensional cases.

Extends results to anisotropic potentials.

Abstract

We prove a quantitative Borg-Levinson theorem for a large class of unbounded potentials. We give a detailed proof when the dimension of the space is greater than or equal to five. We also indicate the modifications necessary to cover lower dimensions. In the last section, we briefly show how to extend our result to the anisotropic case.