On the localization of binding for Schrödinger operators and its extensions to elliptic operators
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 [\textit{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.
scientific article; zbMATH DE number 854437