Transfer functions and local spectral uniqueness for Sturm-Liouville operators, canonical systems and strings (Q2629356)

The paper mostly deals with the Sturm-Liouville operator on an interval \([0,l)\), with a self-adjoint boundary condition at one end. The author shows that the transfer function introduced by M.G. Krein is a powerful tool for proving local versions of the Borg-Marchenko uniqueness theorem, namely, for establishing conditions guaranteeing that two potential coincide on some sub-interval \([0,a]\) with \(a<l\). Particularly, the use of the transfer function simplifies the proof of B. Simon's local versions of the Borg-Marchenko theorem. The application of the transfer function to local spectral uniqueness for other equations, such as canonical systems and string equations, is also discussed.