SPECTRAL THEORY OF PSEUDODIFFERENTIAL-OPERATORS

We define the minimal and maximal operators of an elliptic pseudo-differential operator on L(p)(R(n)), 1 < p < infinity, and prove that they are equal. The spectrum and essential spectra of the minimal (or maximal) operator on L(p)(R(n)), 1 < p < infinity, are then described. Applications of the theory to the self-adjointness and spectral analysis of quantum mechanical observables on L2(R(n)) are given. (C) 1994 Academic Press, Inc.