On complex perturbations of infinite band Schrödinger operators - Kupin, S.; Golinskii, L. (Methods of Functional Analysis and Topology, 2015)
Let H_0=-d^2dx^2+V_0 be an infinite band Schrödinger operator on L^2(R) with a real-valued potential V_0L^∞(R). We study its complex perturbation H=H_0+V, defined in the form sense, and obtain the Lieb-Thirring type inequalities for the rate of convergence of the discrete spectrum of H to the joint essential spectrum. The assumptions on V vary depending on the sign of Re V.