Inverse Problems for Sturm-Liouville Difference Equations - Bohner, Martin; Koyunbakan, Hikmet (Univ Nis, Fac Sci Math, 2016)
We consider a discrete Sturm-Liouville problem with Dirichlet boundary conditions. We show that the specification of the eigenvalues and weight numbers uniquely determines the potential. Moreover, we also show that if the potential is symmetric, then it is uniquely determined by the specification of the eigenvalues. These are discrete versions of well-known results for corresponding differential equations.
Keywords: eigenvalue problem; inverse problem; spectrum; symmetric potential; transformation operator