Dispersive estimate for the Schroedinger equation with point   interactions
  We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove a (weighted) dispersive estimate for the corresponding Schroedinger flow.   In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form. 
Piero D'Ancona and Vittoria Pierfelice and Alessandro Teta