Resonances for Difference Operators

We show the existence of resonances for the difference operators H on l2(Z), defined by D*D + V, where D:φ(n) ↦ φ(n + 1) − φ(n), D*:φ(n) ↦ φ(n) − φ(n − 1), and barrier potential V, multiplication by a real-valued function on Z, supp V ⊂ of [N, N], analogous to the Schrödinger operators, −d2/dx2 + V on L2(R).