Dispersive estimate for the Schroedinger equation with point interactions
Piero D'Ancona, Vittoria Pierfelice, Alessandro Teta
Abstract
We consider the Schroedinger operator in R3 with N point interactions placed at Y=(y1, ... ,yN), yj in R3, of strength a=(a1, ... ,aN). 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.
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