Virtual levels, virtual states, and the limiting absorption principle for higher order differential operators in 1D

Abstract

We consider the resolvent estimates and properties of virtual states of the higher order derivatives in one dimension, focusing on Schroedinger-type operators of degree $N=3$ (the approach applies to higher orders). The derivation is based on the construction of the Jost solution for higher order differential operators and on restricting the resolvent onto subspaces of finite codimension.