Spectral and scattering theory for symmetric systems of nonconstant deficit

Abstract

We study the spectral and scattering problems for symmetric systems of nonconstant deficit. We prove (i) discreteness of eigenvalues, (ii) absolute continuity of continuous spectrum. (iii) principle of limiting absorption. As an application to the scattering problems, the decay of local energy and the completeness of wave operators are obtained. The class of systems we consider here includes the linearized equation of magnetohydrodynamics as a typical example.