Spectral Properties of an Energy-Dependent Hamiltonian

Abstract

We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions [30] and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum. When an additional dissipative or smallness hypothesis is assumed on the potential, we show that the principle of limiting absorption holds at any point of the essential spectrum.