Low-frequency dispersive estimates for the Schrödinger group in higher dimensions

For a large class of real-valued potentials, V (x), x ∈ R, n ≥ 4 , we prove dispersive estimates for the low frequency part of e Pac, provided the zero is neither an eigenvalue nor a resonance of −∆+ V , where Pac is the spectral projection onto the absolutely continuous spectrum of −∆ + V . This class includes potentials V ∈ L(R) satisfying V (x) = O ( 〈x〉−(n+2)/2−ǫ ) , ǫ > 0. As a consequence, we extend the results in [4] to a larger class of potentials.