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Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBONY, Jean Francois
hal.structure.identifierGraduate School of Material Science
dc.contributor.authorFUJIIE, Setsuro
hal.structure.identifierLaboratoire de Mathématiques d'Orsay [LMO]
dc.contributor.authorRAMOND, Thierry
hal.structure.identifierLaboratoire Analyse, Géométrie et Applications [LAGA]
dc.contributor.authorZERZERI, Maher
dc.date.accessioned2024-04-04T02:17:31Z
dc.date.available2024-04-04T02:17:31Z
dc.date.issued2011
dc.identifier.issn0373-0956
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189235
dc.description.abstractEnWe study the spectral projection associated to a barrier-top resonance for the semiclassical Schrodinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of h, and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we give an expansion for large times of the Schrodinger group in terms of these resonances.
dc.language.isoen
dc.publisherAssociation des Annales de l'Institut Fourier
dc.title.enSpectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
dc.typeArticle de revue
dc.identifier.doi10.5802/aif.2643
dc.subject.halMathématiques [math]
bordeaux.journalAnnales de l'Institut Fourier
bordeaux.page1351-1406
bordeaux.volume61
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00994373
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00994373v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20de%20l'Institut%20Fourier&rft.date=2011&rft.volume=61&rft.issue=4&rft.spage=1351-1406&rft.epage=1351-1406&rft.eissn=0373-0956&rft.issn=0373-0956&rft.au=BONY,%20Jean%20Francois&FUJIIE,%20Setsuro&RAMOND,%20Thierry&ZERZERI,%20Maher&rft.genre=article


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