Essential spectrum of perturbed pseudodifferential operators. applications to the schrödinger, Klein-Gordon, and dirac operators

The aim of the paper is to present a new approach to the investigation of the essential spectrum of Schrödinger, Klein-Gordon, and Dirac operators. We include these operators in the class of pseudodifferential operators perturbed by nonsmooth potentials. For an operator under consideration, we introduce a family of limit operators and prove that the essential spectrum of the original operator is the union of the spectra of limit operators. Because the limit operators have a simpler structure than the original operator, we obtain a powerful tool for investigating the essential spectra of differential and pseudodifferential operators. We apply this method to the study of the essential spectrum of the Schrödinger, Klein-Gordon, and Dirac operators.