Skip to Main content Skip to Navigation
New interface
Theses

Etude du spectre discret de perturbations d'opérateurs de la physique mathématique

Abstract : The topic of this thesis concerns the discrete spectrum of non-selfadjoint operators defined by relatively compact perturbation of selfadjoint operators. These selfadjoint operators are choosen among classical operators of quantum mechanics. These areDirac operator, Klein-Gordon operator, and the fractional Laplacian who generalize the Schrödinger operator. The main method is based on a theorem of complex analysis which gives Blaschke-type condition on the zeros of a holomorphic function on the unit disc. This Blaschke condition gives the information on the behaviour of eigenvalues of the perturbed operator by mean of Lieb-Thirring-type inequalities. Another method using functional analysis is also used to obtain these kind of inequalities and both methods are compared to each other.
Document type :
Theses
Complete list of metadata

Cited literature [42 references]  Display  Hide  Download

https://theses.hal.science/tel-01132967
Contributor : ABES STAR :  Contact
Submitted on : Wednesday, March 18, 2015 - 11:57:07 AM
Last modification on : Saturday, December 4, 2021 - 3:43:03 AM
Long-term archiving on: : Monday, April 17, 2017 - 6:38:29 PM

File

DUBUISSON_CLEMENT_2014.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01132967, version 1

Collections

Citation

Clement Dubuisson. Etude du spectre discret de perturbations d'opérateurs de la physique mathématique. Mathématiques générales [math.GM]. Université de Bordeaux, 2014. Français. ⟨NNT : 2014BORD0127⟩. ⟨tel-01132967⟩

Share

Metrics

Record views

216

Files downloads

911