Inverse Problems for Sturm–Liouville Dierence Equations

Abstract

We consider a discrete Sturm{Liouville problem with
Dirichlet boundary conditions. We show that the specication 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 specication of the eigenvalues.
These are discrete versions of well-known results for corresponding
dierential equations.