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 expressions t q : = 1 i ( I 0 0 − I ) d d x + ( 0 q q ⁎ 0 ) and some separated boundary conditions. Here q is an r × r matrix-valued function with entries belonging to L 2 ( ( 0 , 1 ) , C ) and I is the identity r × 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.