Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Spectral Theory Année : 2023

Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators

Résumé

We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting of the Hilbert space and has a variational gap property associated with the block decomposition. A typical example is the Dirac-Coulomb operator defined on C∞(R3 \{0},C4). In this paper we define a distinguished self-adjoint extension with a spectral gap and characterize its eigenvalues in that gap by a min-max principle. This has been done in the past under technical conditions. Here we use a different, geometric strategy, to achieve that goal by making only minimal assumptions. Our result applied to the Dirac-Coulomb-like Hamitonians covers sign-changing potentials as well as molecules with an arbitrary number of nuclei having atomic numbers less than or equal to 137.
Fichier principal
Vignette du fichier
2023-DES (1).pdf (277.92 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03702964 , version 1 (23-06-2022)
hal-03702964 , version 2 (02-02-2023)
hal-03702964 , version 3 (04-04-2023)
hal-03702964 , version 4 (03-08-2023)

Identifiants

Citer

Jean Dolbeault, Maria J Esteban, Eric Séré. Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators. Journal of Spectral Theory, In press. ⟨hal-03702964v3⟩
101 Consultations
51 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More