Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants
| dc.creator | Bouclet, Jean-Marc | |
| dc.creator | Bruneau, Vincent | |
| dc.date | 2007-09-13 | |
| dc.date | 2008-09-11 | |
| dc.date.accessioned | 2026-07-07T10:01:50Z | |
| dc.date.available | 2026-07-07T10:01:50Z | |
| dc.description | 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 (φ_p(z,h)) $ and give semiclassical bounds on $ \partial_z φ_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.description | 37 pages, published version | |
| dc.identifier | https://arxiv.org/abs/0709.2060 | |
| dc.identifier | http://arxiv.org/abs/0709.2060 | |
| dc.identifier | International Mathematics Research Notices 2008 (2008) ID rnn002, 55 pages | |
| dc.identifier | doi:10.1093/irmn/rnn002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168762 | |
| dc.subject | Spectral Theory | |
| dc.subject | 81Q10; 35J10; 47A60 | |
| dc.title | Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants | |
| dc.type | text |