Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants
Language
en
Article de revue
This item was published in
International Mathematics Research Notices. 2008, vol. 2008, p. ID rnn002, 55 pages
Oxford University Press (OUP)
English Abstract
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 $ ...Read more >
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.Read less <
English Keywords
Schrödinger operator
resonances
semi-classical
relative determinant
spectral shift function
scattering
Breit-Wigner
Origin
Hal imported