Inverse resonance scattering on the half line

Abstract

For the Schrödinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one‐to‐one and onto. Moreover, we show that the resonances in any bounded domain in $\mathbb{C}$ _‐ are so‐called free parameters.