Localizations at infinity and essential spectrum of quantum   Hamiltonians: I. General theory
  We isolate a large class of self-adjoint operators H whose essential spectrum is determined by their behavior at large x and we give a canonical representation of their essential spectrum in terms of spectra of limits at infinity of translations of H. The configuration space is an arbitrary abelian locally compact not compact group. 
Vladimir Georgescu, Andrei Iftimovici