Abstract
We consider a natural discretization of the inverse Sturm-Liouville problem ?y?+qy=?ry with Dirichlet boundary conditions. We prove thatq andr are uniquely determined at the mesh points by the eigenvalues of the discrete problem, provided that the number of mesh points is even and thatq andr are even functions around the midpoint of the interval. The corresponding fact is false for the continuous problem. In case the number of mesh points is odd we characterize all solutions of the discrete inverse eigenvalue problem.
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