Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials
| hal.structure.identifier | Laboratoire de Mathématiques de Reims [LMR] | |
| dc.contributor.author | AMOUR, Laurent | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | FAUPIN, Jérémy | |
| hal.structure.identifier | Laboratoire de Mathématiques de Reims [LMR] | |
| dc.contributor.author | RAOUX, Thierry | |
| dc.date.accessioned | 2024-04-04T02:38:57Z | |
| dc.date.available | 2024-04-04T02:38:57Z | |
| dc.date.issued | 2009-03-09 | |
| dc.identifier.issn | 0022-2488 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190922 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.publisher | American Institute of Physics (AIP) | |
| dc.title.en | Inverse spectral results for Schrödinger operators on the unit interval with partial information given on the potentials | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1063/1.3087426 | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| bordeaux.journal | Journal of Mathematical Physics | |
| bordeaux.page | 033505 | |
| bordeaux.volume | 50 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00385838 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00385838v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Physics&rft.date=2009-03-09&rft.volume=50&rft.spage=033505&rft.epage=033505&rft.eissn=0022-2488&rft.issn=0022-2488&rft.au=AMOUR,%20Laurent&FAUPIN,%20J%C3%A9r%C3%A9my&RAOUX,%20Thierry&rft.genre=article |
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