Dispersive estimate for the Schroedinger equation with point interactions.

We consider the Schrödinger operator in ℝ^3 with N point interactions placed at Y=(y_1,…,y_N), y_j ∈ ℝ^3, of strength α=(α_1,…,α_N), α_j ∈ ℝ. Exploiting the spectral theorem and the rather explicit expression for the resolvent we prove the (weighted) dispersive estimate for the corresponding Schrödinger flow. In the special case N=1 the proof is directly obtained from the unitary group which is known in closed form