Geodesic
On the singular spectrum in a system of three particles
Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 283-300 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $H$ be the energy operator of a system of three pairwise interacting particles whose pair potentials admit the estimate $$ |v_\alpha(x)|\leqslant C(1+|x|)^{-a} \qquad a>\frac{11}4,\quad x\in\mathbf R^3, $$ and suppose the subsystems of two particles have no virtual levels. It is established that the singular continuous spectrum of $H$ is empty and its positive eigenvalues have no finite limit points. The considerations of the paper are based on a study of Faddeev's equations in coordinate representation and an application of imbedding theorems for anisotropic Sobolev classes in the space $L_2(\mathbf S^5)$. Bibliography: 13 titles. 
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D. R. Yafaev. On the singular spectrum in a system of three particles. Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 283-300. http://geodesic.mathdoc.fr/item/SM_1979_35_2_a8/

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