  We reformulate all general real coupled self-adjoint boundary value problems
as integral operators and show that they are all finite rank perturbations of
the free space Green's function on the real line. This free space Green's
function corresponds to the nonlocal boundary value problem proposed earlier by
Saito [N. Saito, Appl. Comput. Harmonic Anal., 25, 68--97 (2008)]. We prove
these perturbations to be polynomials of rank up to 4. They encapsulate in a
fundamental way the corresponding boundary conditions.
