On the singular spectrum in a system of three particles

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 $L_2(\mathbf S^5)$.
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