Some properties of threshold eigenstates and resonant states of discrete Schrodinger operators
Some properties of threshold eigenstates and resonant states of discrete Schrodinger operators
复制标题
离散薛定谔算子的阈值本征态和谐振态的一些性质
DOI：
10.1007/s00023-020-00912-6
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发表时间：
2020
影响因子：
1.5
通讯作者：
Kouichi Taira
中科院分区：
文献类型：
--
作者：
Yuji Nomura;Kouichi Taira
我们考虑正方形格点上的三维或更大的离散薛定谔算子。我们证明了椭圆阈值下的共振在无穷远处的渐近行为与连续薛定谔算子的渐近行为相似，并且在双曲阈值下不存在共振。此外，我们还证明了在双曲阈值附近的极限吸收原理。
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.