%0 Journal Article
%T Algebraic spectral gaps
%A Mouchet Amaury
%J ESAIM : Proceedings
%D 2012
%I EDP Sciences
%R 10.1051/proc/201235009
%X For the one-dimensional Schr dinger equation, some real intervals with no eigenvalues (the spectral gaps) may be obtained rather systematically with a method proposed by H. Giacomini and A. Mouchet in 2007. The present article provides some alternative formulation of this method, suggests some possible generalizations and extensively discusses the higher-dimensional case. H. Giacomini et A. Mouchet ont propos¨¦ en 2007 une m¨¦thode permettant d¡¯obtenir des trous spectraux d¡¯un op¨¦rateur de Schr dinger ¨¤ une dimension, c¡¯est-¨¤-dire des intervalles ne contenant aucune valeur propre. Le pr¨¦sent article introduit une formulation diff¨¦rente de cette m¨¦thode, sugg¨¨re des g¨¦n¨¦ralisations possibles et traite de fa on exhaustive le cas de plusieurs dimensions.
%U http://dx.doi.org/10.1051/proc/201235009