In his famous 1981 paper, Mourre gave a sufficient condition for a self-adjoint operator to assure the absence of its singular continuous spectrum. More precisely, consider a self-adjoint operator on a Hilbert space (e.g., with the usual norm), and assume that there is a self-adjoint operator , called a conjugate operator of on an interval , so that
for some positive constant and some compact operator on , where denotes the spectral projection of onto , the commutator , and the inequality is understood in the sense of self-adjoint operators.