Quantitative Borg-Levinson theorem for the magnetic Sch\"odinger operator with unbounded electrical potential

TL;DR

This paper extends a quantitative Borg-Levinson theorem to the magnetic Schr"odinger operator, providing stability estimates for recovering electrical potential and magnetic field from boundary spectral data.

Contribution

It introduces a quantitative stability result for the magnetic Schr"odinger operator, expanding previous work on the unbounded potential case to include magnetic fields.

Findings

H"older stability inequalities for electrical potential recovery

H"older stability inequalities for magnetic field recovery

Extension to both isotropic and anisotropic cases

Abstract

The first author established in [8] a quantitative Borg-Levinson theorem for the Schr\"odinger operator with unbounded potential. In the present work, we extend the results in [8] to the magnetic Schr\"odinger operator. We discuss both the isotropic and anisotropic cases. We establish H\"older stability inequalities of determining the electrical potential or magnetic field from the corresponding boundary spectral data.