Singular continuous Floquet operator for periodic quantum systems

Consider the Floquet operator of a time independent quantum system, acting on a separable Hilbert space, periodically perturbed by a rank one kick: e−iH0Te−iκT|ϕ〉〈ϕ| where T is the period, κ the coupling constant, and H0 is a pure point self-adjoint operator, bounded from below. Under some hypotheses on the vector ϕ, cyclic w.r.t. H0 we prove the following: