Discrete vector Sturm-Liouville problems with non-self-adjoint boundary conditions: Eigenstructure, orthogonality, and eigenfunctions expansion

In this paper, a theory of discrete vector Sturm-Liouville theory for second-order problems where coefficients of the difference equation are scalar and the boundary conditions are not self-adjoint is developed. Eigenstructure, orthogonality, and eigenfunctions expansion are studied and an illustrative example is included.