Self-adjoint extensions for second-order symmetric linear difference equations

In this paper, self-adjoint extensions for second-order symmetric linear difference equations with real coefficients are studied. By applying the Glazman–Krein–Naimark theory for Hermitian subspaces, both self-adjoint subspace extensions and self-adjoint operator extensions of the corresponding minimal subspaces are completely characterized in terms of boundary conditions, where the two endpoints may be regular or singular.