Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants
| hal.structure.identifier | Laboratoire Paul Painlevé - UMR 8524 [LPP] | |
| dc.contributor.author | BOUCLET, Jean-Marc | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRUNEAU, Vincent | |
| dc.date.accessioned | 2024-04-04T02:46:38Z | |
| dc.date.available | 2024-04-04T02:46:38Z | |
| dc.date.issued | 2008 | |
| dc.identifier.issn | 1073-7928 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191572 | |
| dc.description.abstractEn | We prove that the resonances of long range perturbations of the (semiclassical) Laplacian are the zeroes of natural perturbation determinants. We more precisely obtain factorizations of these determinants of the form $ \prod_{w = {\rm resonances}}(z-w) \exp (\varphi_p(z,h)) $ and give semiclassical bounds on $ \partial_z \varphi_p $ as well as a representation of Koplienko's regularized spectral shift function. Here the index $ p \geq 1 $ depends on the decay rate at infinity of the perturbation. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.subject.en | Schrödinger operator | |
| dc.subject.en | resonances | |
| dc.subject.en | semi-classical | |
| dc.subject.en | relative determinant | |
| dc.subject.en | spectral shift function | |
| dc.subject.en | scattering | |
| dc.subject.en | Breit-Wigner | |
| dc.title.en | Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/irmn/rnn002 | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.identifier.arxiv | 0709.2060 | |
| bordeaux.journal | International Mathematics Research Notices | |
| bordeaux.page | ID rnn002, 55 pages | |
| bordeaux.volume | 2008 | |
| 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-00171803 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00171803v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=International%20Mathematics%20Research%20Notices&rft.date=2008&rft.volume=2008&rft.spage=ID%20rnn002,%2055%20pages&rft.epage=ID%20rnn002,%2055%20pages&rft.eissn=1073-7928&rft.issn=1073-7928&rft.au=BOUCLET,%20Jean-Marc&BRUNEAU,%20Vincent&rft.genre=article |
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