Comptes Rendus
no. 12
Functional analysis/Mathematical physics
The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions
[Le spectre essentiel des systèmes à N-corps avec interactions asymptotiquement homogènes d'ordre zéro]

Présenté par : the Editorial Board

Vladimir Georgescu1 ; Victor Nistor2, 3
1 Département de mathématiques, Université de Cergy-Pontoise, 95000 Cergy-Pontoise, France
2 Université de Lorraine, UFR MIM, île du Saulcy, CS 50128, 57045 Metz cedex 01, France
3 Pennsylvania State University, Mathematics Department, University Park, PA 16802, USA
Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1023-1027.

Nous étudions le spectre essentiel des hamiltoniens des systèmes à N corps avec potentiels définis par des fonctions qui ont des limites radiales à l'infini. Les résultats étendent le théorème HVZ, qui décrit le spectre essentiel des hamiltoniens des systèmes à N corps usuels. La preuve de notre théorème principal est basée sur une étude approfondie des algèbres générées par les potentiels avec des limites radiales à l'infini et de leurs produits croisés. Nous décrivons également la topologie sur le spectre de ces algèbres, étendant ainsi à notre cas un résultat de A. Mageira. Nos techniques s'appliquent à des classes plus générales de potentiels associées à des algèbres de fonctions uniformément continues bornées invariantes par translation.

We study the essential spectrum of N-body Hamiltonians with potentials defined by functions that have radial limits at infinity. The results extend the HVZ theorem which describes the essential spectrum of usual N-body Hamiltonians. The proof is based on a careful study of algebras generated by potentials and their cross-products. We also describe the topology on the spectrum of these algebras, thus extending to our setting a result of A. Mageira. Our techniques apply to more general classes of potentials associated with translation invariant algebras of bounded uniformly continuous functions on a finite-dimensional vector space X.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.029
Vladimir Georgescu 1 ; Victor Nistor 2, 3

1 Département de mathématiques, Université de Cergy-Pontoise, 95000 Cergy-Pontoise, France
2 Université de Lorraine, UFR MIM, île du Saulcy, CS 50128, 57045 Metz cedex 01, France
3 Pennsylvania State University, Mathematics Department, University Park, PA 16802, USA 
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     author = {Vladimir Georgescu and Victor Nistor},
     title = {The essential spectrum of {\protect\emph{N}-body} systems with asymptotically homogeneous order-zero interactions},
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     pages = {1023--1027},
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     number = {12},
     year = {2014},
     doi = {10.1016/j.crma.2014.09.029},
     language = {en},
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Vladimir Georgescu; Victor Nistor. The essential spectrum of N-body systems with asymptotically homogeneous order-zero interactions. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1023-1027. doi : 10.1016/j.crma.2014.09.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.029/

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