01416nas a2200169   4500008004100000020002200041245008400063210007000147260004400217300001400261520082100275100002001096700002301116700002901139700002901168856004901197       2017                        eng d  a978-3-319-58904-600aDispersive Estimates for Schrödinger Operators with Point Interactions in ℝ30 aDispersive Estimates for Schrödinger Operators with Point Intera  aChambSpringer International Publishing  a187–1993 a<p>The study of dispersive properties of Schrödinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schrödinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p$−$L^q$ estimates of the free Laplacian in the smaller regime $q \in [2,3)$. These estimates are implied by a recent result concerning the Lpboundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q \geq 3$.</p>1 aIandoli, Felice1 aScandone, Raffaele1 aMichelangeli, Alessandro1 aDell'Antonio, Gianfausto  uhttps://doi.org/10.1007/978-3-319-58904-6_11