Dispersive estimate for the Schroedinger equation with point interactions
偏微分方程分析
2009-11-11 v1
摘要
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.
引用
@article{arxiv.math/0509704,
title = {Dispersive estimate for the Schroedinger equation with point interactions},
author = {Piero D'Ancona and Vittoria Pierfelice and Alessandro Teta},
journal= {arXiv preprint arXiv:math/0509704},
year = {2009}
}
备注
12 pages