On a condition of the absence of a singular continuous spectrum for the Friedrichs model

An extension of the analytic dilation or the Mourre commutators methods is proposed. We consider two self-adjoints operators $H=H_0+V$ and $A$. Assuming some smouthness properties of $V$ and $[V, A]$ we prove the absence of singular continuous spectrum of $H$. No positivity of $[H_0, V]$ is required.