Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants

dc.creatorBouclet, Jean-Marc
dc.creatorBruneau, Vincent
dc.date2007-09-13
dc.date2008-09-11
dc.date.accessioned2026-07-07T10:01:50Z
dc.date.available2026-07-07T10:01:50Z
dc.descriptionWe 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.description37 pages, published version
dc.identifierhttps://arxiv.org/abs/0709.2060
dc.identifierhttp://arxiv.org/abs/0709.2060
dc.identifierInternational Mathematics Research Notices 2008 (2008) ID rnn002, 55 pages
dc.identifierdoi:10.1093/irmn/rnn002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168762
dc.subjectSpectral Theory
dc.subject81Q10; 35J10; 47A60
dc.titleSemiclassical Resonances of Schrödinger operators as zeroes of regularized determinants
dc.typetext

Files

Collections