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Dispersive estimates for Schrödinger operators with point interactions in R3

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dc.contributor.author Iandoli, Felice
dc.contributor.author Scandone, Raffaele
dc.date.accessioned 2017-03-30T07:24:16Z
dc.date.available 2017-03-30T07:24:16Z
dc.date.issued 2017-03-30
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/35277
dc.description.abstract 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 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.language.iso en en_US
dc.relation.ispartofseries SISSA;01/2017/MATE
dc.title Dispersive estimates for Schrödinger operators with point interactions in R3 en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 12 en_US


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