The limiting absorption principle and spectral theory for steady-state wave propagation in globally perturbed nonselfadjoint media

Abstract

A fundamental problem in classical physics is to describe the waves produced in a medium by the action of prescribed sources. When such sources have a sinusoidal time dependence (as is frequently postulated), the resulting waves may be expected to have the same oscillatory behavior in time, apart from a transient wave. The problem of determining this steadystate response is usually called the steady-state wave propagation problem. This paper deals with the steady-state propagation problem for electromagnetic waves in a class of globally perturbed nonselfadjoint media. Here, we shall consider the problem in a certain subspace of inhomogeneous data. Systems other than Maxwell’s equations may be treated using the methods of this paper and such will be the subject of future work. Up to this point integral (global) perturbations of Maxwell’s equations have received little consideration, to our knowledge. Our problem is a special case of the more general problem