The Uniqueness of Inverse Problem for the Dirac Operators with Partial Information

The inverse spectral problem for the Dirac operators defined on the interval[0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of potentials(p(x), r(x)) and a boundary condition are uniquely determined even if only partial information is given on(p(x), r(x))together with partial information on the spectral data, consisting of either one full spectrum and a subset of norming constants, or a subset of pairs of eigenvalues and the corresponding norming constants. Moreover, the authors are also concerned with the situation where both p(x) and r(x) are C n-smoothness at some given point.