An inverse eigenvalue problem for one dimensional Dirac operators (Q1677601)

The inverse spectral problem is studied for the boundary value problem \[ \begin{bmatrix} 0 & 1 \cr -1 & 0 \end{bmatrix} Y'(x)+ \begin{bmatrix} q(x)+m & 0 \cr 0 & q(x)-m \end{bmatrix} Y(x)=\lambda Y(x),\; Y(x)= \begin{bmatrix} y_1(x) \cr y_2(x)\end{bmatrix} , \; 0<x<\pi, \] \[ y_1(0)\cos\alpha+y_2(0)\sin\alpha=0,\; y_1(\pi)\cos\beta+y_2(\pi)\sin\beta=0. \] Fix \(d\in(0,\pi).\) Under additional assumptions it is proved that the specification of the spectrum uniquelly determines \(q(x)\) on \((0,d)\) provided that \(q(x)\) is known a priori on \((d,\pi).\)