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Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials

hal.structure.identifierLaboratoire de Mathématiques de Reims [LMR]
dc.contributor.authorAMOUR, Laurent
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorFAUPIN, Jérémy
hal.structure.identifierLaboratoire de Mathématiques de Reims [LMR]
dc.contributor.authorRAOUX, Thierry
dc.date.accessioned2024-04-04T02:38:57Z
dc.date.available2024-04-04T02:38:57Z
dc.date.issued2009-03-09
dc.identifier.issn0022-2488
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190922
dc.description.abstractEnWe pursue the analysis of the Schrödinger operator on the unit interval in inverse spectral theory initiated in the work of Amour and Raoux ["Inverse spectral results for Schrödinger operators on the unit interval with potentials in $L^p$ spaces", Inverse Probl. 23, 2367 (2007)]. While the potentials in the work of Amour and Raoux belong to $L^1$ with their difference in $L^p$, $1 \le p < +\infty$, we consider here potentials in $W^{k,1}$ spaces having their difference in $W^{k, p}$, where $1 \le p \le + \infty$, $k \in \{0 , 1 , 2\}$. It is proved that two potentials in $W^{k,1}([0,1])$ being equal on $[a,1]$ are also equal on $[0,1]$ if their difference belongs to $W^{k, p}([0,a])$ and if the number of their common eigenvalues is sufficiently high. Naturally, this number decreases as the parameter $a$ decreases and as the parameters $k$ and $p$ increase.
dc.language.isoen
dc.publisherAmerican Institute of Physics (AIP)
dc.title.enInverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials
dc.typeArticle de revue
dc.identifier.doi10.1063/1.3087426
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
bordeaux.journalJournal of Mathematical Physics
bordeaux.page033505
bordeaux.volume50
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00385838
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00385838v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Journal%20of%20Mathematical%20Physics&amp;rft.date=2009-03-09&amp;rft.volume=50&amp;rft.spage=033505&amp;rft.epage=033505&amp;rft.eissn=0022-2488&amp;rft.issn=0022-2488&amp;rft.au=AMOUR,%20Laurent&amp;FAUPIN,%20J%C3%A9r%C3%A9my&amp;RAOUX,%20Thierry&amp;rft.genre=article


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