Some new results on weak compactness

We consider the scattering problem in Lsu2$\text{Rsu3}$ for Schrödinger operators with momentum-dependent interactions, i.e., for the pair of Hamiltonians H₀ = ? Δ and H = H₀ + T, where T is a pseudodifferential operator. The existence of the wave operators is proved by estimating the integrals appearing in the CookHack convergence criterion, and their asymptotic completeness is established under more restrictive conditions on the symbol of T by using a local trace criterion.