Spectral Theory of Pseudo-Differential Operators

AbstractWe define the minimal and maximal operators of an elliptic pseudo-differential operator on Lp(Rn), 1 < p < ∞, and prove that they are equal. The spectrum and essential spectra of the minimal (or maximal) operator on Lp(Rn), 1 < p < ∞, are then described. Applications of the theory to the self-adjointness and spectral analysis of quantum mechanical observables on L2(Rn) are given