On the Mourre estimates for Floquet Hamiltonians

In the spectral and scattering theory for a Schrodinger operator with a time-periodic potential $$H(t)=p^2/2+V(t,x)$$ , the Floquet Hamiltonian $$K=-i\partial _t+H(t)$$ associated with H(t) plays an important role frequently, by virtue of the Howland–Yajima method. In this paper, we introduce a new conjugate operator for K in the standard Mourre theory, that is different from the one due to Yokoyama, in order to relax a certain smoothness condition on V.