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Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique

Olivier Lablée (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Dans cette article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.

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