Essential spectrum of pseudodifferential operators with operator-valued symbols (Q653036)

The author considers the Fredholm property of the essential spectrum of pseudodifferential operators with operator-valued symbols for which the study of the Fredholm property is reduced to the analysis of their local invertibility at infinity by means of the method of limit operators of the author et al. This method has proved to be an effective tool for the study of the essential spectrum of operators in quantum mechanics, their discrete models, and the behavior of eigenfunctions of the discrete spectrum at infinity. An application to quantum wave guides is considered. Two types of electric potentials are analyzed in detail: (i) slowly oscillating at infinity and (ii) perturbation of periodic potentials by slowly oscillating ones.