Inverse spectral problems for Dirac operators on a finite interval

We consider the direct and inverse spectral problems for Dirac operators that are generated by the differential expressionstq:=1i(I00−I)ddx+(0qq⁎0) and some separated boundary conditions. Here q   is an r×rr×r matrix-valued function with entries belonging to L2((0,1),C)L2((0,1),C) and I   is the identity r×rr×r matrix. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest an algorithm of reconstructing the potential q from the corresponding spectral data.