Stability of an Inverse Problem in Potential Scattering on the Real Line

In the later part of the paper we shall assume in addition that p decays exponentially at −∞. The support properties of the potential imply that the right reflection coefficient r(k) admits a meromorphic continuation to the upper half-plane C+ = {k ∈ C, Im k > 0} with at most finitely many poles. The inverse problem under consideration consists of recovery of the potential p from the sequence {r(in), n = 1, 2 . . .}. This sequence will be referred to as “the data”. We remark that part of the motivation for studying this problem comes from an inverse boundary value problem for the Schrödinger operator with radially symmetric potential in two dimensions. We refer to the paper by J.