论文标题
具有整数值势的离散Schrödinger操作员的半线压缩和有限段
Half-line compressions and finite sections of discrete Schrödinger operators with integer-valued potentials
论文作者
论文摘要
我们研究1D离散的Schrödinger运营商$ h $具有整数价值的潜力，并表明，$（i）$，$ H $的可逆性（实际上，甚至是Fredholmness）的$ h $总是意味着其半线压缩$ h _+$（零dirichlet边界条件，即矩阵截止）。尤其是，Dirichlet特征值避免了零 - 以及所有其他整数。我们使用此结果得出结论，$（ii）$，有限部分方法（通过有限和生长矩阵截断的大约反转）适用于$ h $，只要$ h $是可逆的。对于$ h _+$，也是如此。
We study 1D discrete Schrödinger operators $H$ with integer-valued potential and show that, $(i)$, invertibility (in fact, even just Fredholmness) of $H$ always implies invertibility of its half-line compression $H_+$ (zero Dirichlet boundary condition, i.e. matrix truncation). In particular, the Dirichlet eigenvalues avoid zero -- and all other integers. We use this result to conclude that, $(ii)$, the finite section method (approximate inversion via finite and growing matrix truncations) is applicable to $H$ as soon as $H$ is invertible. The same holds for $H_+$.
