Consider the Sturm-Liouville problem given by the equation on and the boundary condition . The famous Borg-Marchenko theorem states that the associated Weyl-Titchmarsh -function determines uniquely the potential when is real. The local version states that is determined on if the -function is known up to errors of the order of (where is positive) as tends to infinity along some non-real ray.
We show that under certain very general restrictions on an analogous result holds also for complex-valued potentials.
This is joint work with B. M. Brown and R. A. Peacock.