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.
We study the asymptotic behavior for the eigenvalues of Sturm-Liouville operators with smooth potential.The precise asymptotic expressions for the eigenvalues of the operators with general boundary conditions are given.
Yan Wang,Guangsheng Wei (College of Math.and Information Science,Shaanxi Normal University,Xi’an 710062)
