Properties of the Scattering Transform on the Real Line

Abstract

Continuity properties of the scattering transform associated to the Schrödinger operator on the real line are studied. Stability estimates of Lipschitz type are derived for the scattering and inverse scattering transforms.

Inverse spectral theory as influenced by Barry Simon

“…Then combining (6.125) with (6.80) yields Simon's inverse spectral approach as an alternative to that by Gel'fand and Levitan: More recent references: Local solvability and a necessary condition for global solvability of the A-equation (6.119) were recently discussed by Zhang [252], [253]. Connections between the A-amplitude and the scattering transform for Schrödinger operators on the real line have been discussed by Hitrik [117].…”