The local Borg–Marchenko uniqueness theorem for Dirac-type systems with locally smooth at the right endpoint rectangular potentials

Abstract

We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, b), where \(0<b\le \infty .\) We present a new proof of the local Borg–Marchenko uniqueness theorem. The high-energy asymptotics of the Weyl–Titchmarsh functions and the local Borg–Marchenko uniqueness theorem are derived for locally smooth potentials at the right endpoint.