Inverse Problems for Difference Equations with Quadratic Eigenparameter Dependent Boundary Conditions-II

Abstract

The following inverse problem is solved—given the eigenvalues and the potential b(n) for a difference boundary value problem with quadratic dependence on the eigenparameter, λ , the weights c(n) can be uniquely reconstructed. The investi-gation is inductive on m where represents the number of unit intervals and the results obtained depend on the specific form of the given boundary conditions. This paper is a sequel to [1] which provided an algorithm for the solution of an analogous inverse problem, where the eigenvalues and weights were given and the potential was uniquely reconstructed. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in [1], an additional spectrum is required more often than was the case in [1].