On the Polynomial and Exponential Decay of Eigen-Forms of Generalized Time-Harmonic Maxwell Problems

TL;DR

This paper proves polynomial and exponential decay of eigen-forms for generalized Maxwell operators in exterior domains, ensuring non-accumulation of eigenvalues and establishing a Fredholm alternative via the limiting absorption principle.

Contribution

It demonstrates decay properties of eigen-forms for Maxwell systems with complex coefficients and confirms spectral properties like non-accumulation of eigenvalues.

Findings

Eigen-forms decay polynomially and exponentially at infinity.

Eigen-values do not accumulate in R ackslash {0}.

A Fredholm alternative holds via the limiting absorption principle.

Abstract

We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. As a canonical application we show that the corresponding eigen-values do not accumulate in R \ {0} and that by means of Eidus' limiting absorption principle a Fredholm alternative holds true.