Abstract
In this paper, we study the residue of the scattering amplitude for the Schrödinger operator with long-range perturbation of the Laplacian, in the case where there are resonances exponentially close to the real axis. If the resonances are simple and under a separation condition, one proves that the residue of the scattering amplitude associated with a resonance ξ is bounded by C(h)|Im ξ|. Here C(h) denotes an explicit constant depending polynomially on h−1 and the number of resonances in a fixed box. This generalizes a recent result of Stefanov concerning compactly supported perturbations and isolated resonances.
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