Properties of the scattering map. II (Q909084)

Summary: This paper continues the investigation of the scattering map as it was started in ibid. 61, 442-480 (1986; Zbl 0595.34027)]. Again we consider the Schrödinger equation \[ -\frac{d^ 2}{dx^ 2}y(x)+q(x)y(x)=k^ 2y(x) \] on the whole line where q is a real valued potential in the weighted Sobolev space \(H_{N,N}\) (N\(\geq 3)\). The aim of this paper is to extend the study of the map SD, associating to a potential q its scattering data for the case where q has bound states.