Schrödinger Flow’s Dispersive Estimates in a regime of Re-scaled Potentials

Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The problem of monitoring the (constants in the estimates that quantify the) dispersive behaviour of the flow generated by a Schrödinger operator is posed in terms of the scaling parameter that expresses the small size of the support of the potential, along the scaling limit towards a Hamiltonian of point interaction. At positive size, dispersive estimates are completely classical, but their dependence on the short range of the potential is not explicit, and the understanding of such a dependence would be crucial in connecting the dispersive behaviour of the short-range Schrödinger operator with the zero-range Hamiltonian. The general set-up of the problem is discussed, together with preliminary answers, open questions, and plausible conjectures, in a ‘propaganda’ spirit for this subject.

Original languageEnglish
Title of host publicationSpringer INdAM Series
PublisherSpringer-Verlag Italia s.r.l.
Pages111-125
Number of pages15
DOIs
Publication statusPublished - 2022

Publication series

NameSpringer INdAM Series
Volume52
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

ASJC Scopus subject areas

  • Mathematics(all)

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