Wave Support Theorem and Inverse Resonant Uniqueness on the Line

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.