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On the localization of binding for Schrödinger operators and its extensions to elliptic operators. (English) Zbl 0859.35082
The lowest eigenvalue \(E(R)\) of perturbations of the \(n\)-dimensional Laplacian \(-\Delta+V(x)+W(x-R)\) is studied for large \(R\). The quantity is important in the discussion of the Efimov effect [H. Tamura, J. Funct. Anal. 95, No.. 2, 433-459 (1991; Zbl 0761.35078)]. The main results are the bounds \(-C_1\leq R^{n-2}E(R)\leq-C_2\) in the case \(n\geq 5\) with assumptions on the decay of \(V\) and \(W\) which are in some sense optimal. The results are generalized to perturbations of equivariant operators for more general group actions on a manifold.
Reviewer: J.Asch (Marseille)

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35B20 Perturbations in context of PDEs
35Q40 PDEs in connection with quantum mechanics
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