Spectra and pseudospectra of non-selfadjoint operators
type: Dataset
description: Spectral instability of non-selfadjoint operators is the main subject of this thesis. Our first goal is to understand the pseudospectral behavior of natural models such as the complex Airy operator, harmonic oscillator and cubic oscillator. To this purpose, we analyze the asymptotic behavior of the spectral projections associated with the eigenvalues of these operators, following a work initiated by E.B. Davies. Our second goal is to illustrate how such models can be used in several problems arising in quantum mechanics, superconductivity or control theory. For instance, our results on the spectral instability of the complex cubic oscillator enable us to confirm that the current theory of non-hermitian quantum mechanics can not be rigorously justified, as recently pointed out by B. Krejcirik and P. Siegl. On the other hand, we obtain spectral information and resolvent estimates for semi-classical Schrödinger operators with purely imaginary potentials in a bounded domain, by using the properties of the models mentioned above. In particuler, these results entail some information on the time-dependent Ginzburg-Landau system in superconductivity. Finally, we reproduce a joint work with K. Beauchard, B. Helffer et L. Robbiano in which the controllability of some degenerate parabolic operators is investigated. An analysis of the spectrum and resolvent of the complex Airy operator and harmonic oscillator yields some controllability and non-controllability results for the equation under consideration.
identifier: NNT: 2013PA112284
issued: 2026-05-07T15:25:50.139451
language: fr
modified: 2026-05-07T15:25:50.139456
contact point: Organization
  fn: CCSD
keyword: anharmonic-oscillators
keyword: complex-wkb-estimates
keyword: estimations-wkb-complexes
keyword: infoeu-reposemanticsdoctoralthesis
keyword: instabilite-spectrale
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: non-selfadjoint-operators
keyword: operateurs-non-autoadjoints
keyword: operateurs-pt-symetriques
keyword: oscillateurs-anharmoniques
keyword: projecteurs-spectraux
keyword: pt-symmetric-operators
keyword: spectral-instability
keyword: spectral-projections
keyword: supraconductivite
keyword: supraconductivity
keyword: theses
landing page: https://theses.hal.science/tel-00924425

Spectra and pseudospectra of non-selfadjoint operators
type: Distribution
format: HTML
issued: 2026-05-07T15:25:50.156881
modified: 2026-05-07T15:25:50.121853
access URL: https://theses.hal.science/tel-00924425

test_moissonnage_selune
type: Agent