Title :

Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants

Author(s) :

Bouclet, Jean-Marc [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Bruneau, Vincent [Auteur]
Institut de Mathématiques de Bordeaux [IMB]

Journal title :

International Mathematics Research Notices

Pages :

ID rnn002, 55 pages

Publisher :

Oxford University Press (OUP)

Publication date :

2008

ISSN :

1073-7928

English keyword(s) :

Schrödinger operator
resonances
semi-classical
relative determinant
spectral shift function
scattering
Breit-Wigner

HAL domain(s) :

Mathématiques [math]/Théorie spectrale [math.SP]

English abstract : [en]

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 $ ...
Show 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.Show less >

Language :

Anglais

Popular science :

Non

Comment :

37 pages, published version

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL