Algebraic spectral gaps
نویسنده
چکیده
For the one-dimensional Schrödinger 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 proposé en 2007 une méthode permettant d’obtenir des trous spectraux d’un opérateur de Schrödinger à une dimension, c’est-à-dire des intervalles ne contenant aucune valeur propre. Le présent article introduit une formulation différente de cette méthode, suggère des généralisations possibles et traite de façon exhaustive le cas de plusieurs dimensions.
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