Semiclassical estimates of the cut-off resolvent for trapping perturbations
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONY, Jean-Francois | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| dc.date.accessioned | 2024-04-04T02:19:43Z | |
| dc.date.available | 2024-04-04T02:19:43Z | |
| dc.date.created | 2012-09-21 | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 1664-039X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189429 | |
| dc.description.abstractEn | This paper is devoted to the study of a semiclassical "black box" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the unphysical sheet with $- h |ln h| < Im z < 0$, we prove that this estimate holds with a constant $h |Im z|^{-1} e^{C|Im z|/h}$. We also obtain analogous bounds for the resonances states of $P$. These results hold without any assumption on the trapped set neither any assumption on the multiplicity of the resonances. | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.title.en | Semiclassical estimates of the cut-off resolvent for trapping perturbations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4171/JST/49 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1201.5573 | |
| bordeaux.journal | Journal of Spectral Theory | |
| bordeaux.page | 399-422 | |
| bordeaux.volume | 3 | |
| 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-00947021 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00947021v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Spectral%20Theory&rft.date=2013&rft.volume=3&rft.spage=399-422&rft.epage=399-422&rft.eissn=1664-039X&rft.issn=1664-039X&rft.au=BONY,%20Jean-Francois&PETKOV,%20Vesselin&rft.genre=article |
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