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

We consider self-adjoint Dirac-type systems with rectangular matrix potentials on the interval [0, b),  where 0<b≤∞.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<b\le \infty .$$\end{document} 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.