On the eigenvalues of operators with gaps. Application to Dirac operators.
Dolbeault, Jean ; Esteban, Maria J. ; Séré, Eric
HAL, hal-00659883 / Harvested from HAL
Text on HAL
This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a Coulomb-like potential. The result is optimal for the Coulomb potential.
Publié le : 2000-07-05
Classification:  variational methods,  self-adjoint operators,  quadratic forms,  spectral gaps,  eigenvalues,  min-max,  Rayleigh Ritz quotients,  Dirac operators,  Hardy's inequality,  [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00659883,
     author = {Dolbeault, Jean and Esteban, Maria J. and S\'er\'e, Eric},
     title = {On the eigenvalues of operators with gaps. Application to Dirac operators.},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00659883}
}

Dolbeault, Jean; Esteban, Maria J.; Séré, Eric. On the eigenvalues of operators with gaps. Application to Dirac operators.. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00659883/