On the spectral properties of non-selfadjoint discrete Schrödinger operators (Q2193427)

The authors consider a (non self-adjoint) compact perturbation \(V\) of a purely absolutely continuous self-adjoint operator \(H_0\) acting on a separable infinite-dimensional Hilbert space. Their model operator \(H_0\) is the discrete Schrödinger operator in dimension one. They study how the regularity properties of \(V\) relate to the spectral properties of \(H_0+V\), in particular the existence of LAP (Limiting Absorption Principles) and the distribution of the discrete spectrum. For highly regular \(V\) they show that the limit points of the discrete spectrum of \(H_0+V\) are necessarily contained in the set of thresholds of \(H_0\) and conclude that the discrete spectrum is finite. For mildly regular \(V\) they show that the set of embedded eigenvalues away from the thresholds is finite and they exhibit some restricted versions of LAP.