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Dispersive estimate for the Schroedinger equation with point interactions

Piero D'Ancona·Vittoria Pierfelice·Alessandro Teta
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Abstract

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.

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Piero D'Ancona, Vittoria Pierfelice, Alessandro Teta. 2005-09-29. Dispersive estimate for the Schroedinger equation with point interactions. https://doi.org/10.1002/mma.682

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