The inverse resonance problem for perturbations of algebro-geometric potentials

TL;DR

This paper demonstrates that for certain Schrödinger operators, the potential can be uniquely reconstructed from the spectral data comprising Dirichlet eigenvalues and resonances, specifically for perturbations of algebro-geometric potentials.

Contribution

It establishes a uniqueness result for the inverse resonance problem in the context of perturbations of algebro-geometric potentials on the half line.

Findings

Unique determination of potentials from spectral data.

Extension of inverse spectral theory to algebro-geometric potentials.

Applicable to compactly supported perturbations.

Abstract

We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues and resonances.