General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators

Dolbeault, Jean, Esteban, Maria, and Séré, Eric. "General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators." Journal of the European Mathematical Society 008.2 (2006): 243-251. <http://eudml.org/doc/277252>.

@article{Dolbeault2006,
abstract = {This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.},
author = {Dolbeault, Jean, Esteban, Maria, Séré, Eric},
journal = {Journal of the European Mathematical Society},
keywords = {essential spectrum; eigenvalues; spectral gaps; variational methods; Rayleigh Ritz quotients; self-adjoint operator; form domain; Dirac operator with a Coulomb-like potential; essential spectrum; eigenvalues; spectral gaps; variational methods; Rayleigh Ritz quotients; self-adjoint operator; form domain; Dirac operator with a Coulomb-like potential},
language = {eng},
number = {2},
pages = {243-251},
publisher = {European Mathematical Society Publishing House},
title = {General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators},
url = {http://eudml.org/doc/277252},
volume = {008},
year = {2006},
}

TY - JOUR
AU - Dolbeault, Jean
AU - Esteban, Maria
AU - Séré, Eric
TI - General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators
JO - Journal of the European Mathematical Society
PY - 2006
PB - European Mathematical Society Publishing House
VL - 008
IS - 2
SP - 243
EP - 251
AB - This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.
LA - eng
KW - essential spectrum; eigenvalues; spectral gaps; variational methods; Rayleigh Ritz quotients; self-adjoint operator; form domain; Dirac operator with a Coulomb-like potential; essential spectrum; eigenvalues; spectral gaps; variational methods; Rayleigh Ritz quotients; self-adjoint operator; form domain; Dirac operator with a Coulomb-like potential
UR - http://eudml.org/doc/277252
ER -