Resonances for difference operators (Q1900342)

The author shows the existence of resonances for the difference operators \(H\) on \(\ell^2(\mathbb{Z})\), defined by \(D^* D+ V\), where \(D: \varphi(n)\mapsto \varphi(n+ 1)- \varphi(n)\), \(D^*: \varphi(n)\mapsto \varphi(n)- \varphi(n- 1)\), and barrier potential \(V\), multiplication by a real-valued function on \(\mathbb{Z}\), \(\text{supp } V\subset [N, N]\), analogous to the Schrödinger operators, \(-d^2/dx^2+ V\) on \(L^2(\mathbb{R})\).