Wave Support Theorem and Inverse Resonant Uniqueness on the Line

TL;DR

This paper investigates the inverse problem related to resonant scattering on the line, analyzing wave structures and establishing partial uniqueness results using complex analysis techniques.

Contribution

It introduces a novel approach to inverse resonant scattering problems by leveraging the structure of perturbed waves and Nevanlinna theory for partial uniqueness.

Findings

Estimation of the common part of perturbed waves and their Fourier transforms.

Partial inverse uniqueness derived from Nevanlinna type representation.

Analysis of the structure of perturbed linear waves.

Abstract

In the paper, we experimentally study the inverse problem with the resonant scattering determinant. We analyze the structure of characteristics of perturbed linear waves. Assuming there is the common part of potential perturbation propagating along the same strips, we estimate the common part of the perturbed wave, and its Fourier transform. We deduce the partial inverse uniqueness from the Nevanlinna type of representation theorem.