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Limiting absorption principle for discrete Schrödinger operators with a Wigner-von Neumann potential and a slowly decaying potential
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GOLENIA, Sylvain | |
| hal.structure.identifier | Independent Researcher | |
| dc.contributor.author | MANDICH, Marc-Adrien | |
| dc.date.accessioned | 2024-04-04T02:49:14Z | |
| dc.date.available | 2024-04-04T02:49:14Z | |
| dc.date.issued | 2021-01 | |
| dc.identifier.issn | 1424-0637 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191805 | |
| dc.description.abstractEn | We consider discrete Schrödinger operators on ${\mathbb{Z}}^d$ for which the perturbation consists of the sum of a long-range type potential and a Wigner-von Neumann type potential. Still working in a framework of weighted Mourre theory, we improve the limiting absorption principle (LAP) that was obtained in [Ma1]. To our knowledge, this is a new result even in the one-dimensional case. The improvement consists in a weakening of the assumptions on the long-range potential and better LAP weights. The improvement relies only on the fact that the generator of dilations (which serves as conjugate operator) is bounded from above by the position operator. To exploit this, Loewner's theorem on operator monotone functions is invoked. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | 2010 Mathematics Subject Classification. 39A70 | |
| dc.subject.en | 81Q10 | |
| dc.subject.en | 47B25 | |
| dc.subject.en | 47A10 limiting absorption principle | |
| dc.subject.en | discrete Schrödinger operator | |
| dc.subject.en | Wigner-von Neumann potential | |
| dc.subject.en | Mourre theory | |
| dc.subject.en | weighted Mourre theory | |
| dc.subject.en | Loewner's theorem | |
| dc.subject.en | polylogarithms | |
| dc.title.en | Limiting absorption principle for discrete Schrödinger operators with a Wigner-von Neumann potential and a slowly decaying potential | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00023-020-00971-9 | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 2002.04909 | |
| bordeaux.journal | Annales Henri Poincaré | |
| bordeaux.page | 83-120 | |
| bordeaux.volume | 22 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02474104 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02474104v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annales%20Henri%20Poincar%C3%A9&rft.date=2021-01&rft.volume=22&rft.issue=1&rft.spage=83-120&rft.epage=83-120&rft.eissn=1424-0637&rft.issn=1424-0637&rft.au=GOLENIA,%20Sylvain&MANDICH,%20Marc-Adrien&rft.genre=article |
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