General conditions have been
found which imply that the perturbation A + q of an elliptic differential operator A
by a singular potential term q(x) has a closed extension B in L2(Rn) having the
same essential spectrum as A. The purpose of this paper is to sharpen the
known results slightly and to estimate the characteristic numbers of the
operator (A + λ)p− (B + λ)p. Under an appropriate assumption on q(x), this
operator is shown to be of trace class for large p. In the self-adjoint case it
follows then from results of Kato that wave operators for the pair (A,B) exist
and that the absolutely continuous parts of these operators are unitarily
equivalent.
