Inverse Sturm-Liouville Problems with a Class of Non-Self-Adjoint Boundary Conditions Containing the Spectral Parameter

The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated. Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems, some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions. To best understand the result, an algorithm and some examples are posted.