We consider for discrete Schrödinger operators with dimension three or larger on the square lattice. We prove that the asymptotic behavior at infinity of resonances at elliptic thresholds is similar to those of continuous Schrödinger operators and that resonances are absent at hyperbolic thresholds. Moreover, we show the limiting absorption principle near the hyperbolic thresholds with the optimal weight.

中文翻译：

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离散薛定ding算子的阈值本征态和共振态的某些性质

我们考虑在正方形晶格上维数为3或更大的离散Schrödinger算子。我们证明了在椭圆阈值处的共振无限处的渐近行为与连续薛定ding算子的相似，并且在双曲阈值处不存在共振。此外，我们在具有最佳权重的双曲阈值附近显示了极限吸收原理。