Remark 6.5.6 states that we have a homeomorphism E S (X) ? ?(X) ,
, We obtain the following result for the spaces
, This corresponds to potentials that have limit 0 on X/Y . The spectrum of this algebra (after we adjoin a unit) identifies with the closure of the image of X in Y ?S (X/Y ) + , where Z + denotes the one point compactification of a locally compact space, Z. Since A S ? E S (X)
, Generally, the topology on A S is rather complicated and singular
, we take X := R 3N and consider the subspaces P j and P ij of Equation (1.5) We let F be the semilattice generated by the subspaces P i and P ij , i, j ? {1, 2, . . . , N }. Let S be the finite semilattice of p-submanifolds of X
, S] will be endowed with natural smooth actions of X := R 3N by translation, of S N , the symmetric group on N variables, by permutation, and O(3) acting diagonally on the components of X := R 3N
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Résumé Nous étudions l'opérateur H = ?? + V qui représente l'énergie d'un système à N -électrons. Pour cela, nous utilisons les algèbres d'opérateurs. Nous commençons par définir une C * -algèbres A qui contient le potentiel V du problème puis nous prenons son produit croisé A X . Les résolvantes de H sont ainsi contenues dans cette C * -algèbre dans A X. Par une étude précise du spectre de A X, nous obtenons une décomposition spectrale essentiel de H et donc un résultat qui étend le théorème HVZ dans la continuité des travaux de V. Georgescu. Nous étendons ce résultat en remplaçant l'espace euclidien X par le groupe de Heisenberg. Dans la seconde partie de la thèse, nous montrons que le spectre de la C * ?algèbre A et un espace introduit par A. Vasy dans les années 2000 sont les mêmes. L'espace construit par A. Vasy est construit par éclatements successifs d'une variété différentielle à coins. La preuve repose également sur des résultats d'éclatements de variétés, Comm. Math. Phys, vol.136, issue.2, pp.399-432, 1991. ,