Dispersive estimates for Schrödinger operators with point interactions in R3

dc.contributor.areaMathematicsen_US
dc.contributor.authorIandoli, Felice
dc.contributor.authorScandone, Raffaele
dc.date.accessioned2017-03-30T07:24:16Z
dc.date.available2017-03-30T07:24:16Z
dc.date.issued2017-03-30
dc.description.abstractThe 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 R3, the perturbed Laplacian satisfies the same Lp -Lq estimates of the free Laplacian in the smaller regime q ∈ 2 [2;3). These estimates are implied by a recent result concerning the Lp boundedness 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 ≥ 3.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35277
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;01/2017/MATE
dc.relation.lastpage12en_US
dc.titleDispersive estimates for Schrödinger operators with point interactions in R3en_US
dc.typePreprinten_US
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