论文标题
在一般晶格上的离散Schrödinger运营商的Isozaki-Kitada修饰符的构建
Construction of Isozaki-Kitada modifiers for discrete Schrödinger operators on general lattices
论文作者
论文摘要
我们考虑了$ \ Mathcal {h} = \ ell^2（\ Mathbb {z}^d; \ Mathbb {C}^n）$扰乱的散射理论，该理论均具有远距离潜在的$ v：\ Mathbb {z}^d \ to \ to \ to \ m athbb {r}^n $。激励人物之一是$ \ mathbb {z}^d $ - periodic图的离散schrödinger运算符。我们构建了独立于时间的修饰符，所谓的Isozaki-kitada修饰符，我们证明了具有上述异萨基 - 吉他修饰符的修饰波运算符，并且它们已完成。
We consider a scattering theory for convolution operators on $\mathcal{H}=\ell^2(\mathbb{Z}^d; \mathbb{C}^n)$ perturbed with a long-range potential $V:\mathbb{Z}^d\to\mathbb{R}^n$. One of the motivating examples is discrete Schrödinger operators on $\mathbb{Z}^d$-periodic graphs. We construct time-independent modifiers, so-called Isozaki-Kitada modifiers, and we prove that the modified wave operators with the above-mentioned Isozaki-Kitada modifiers exist and that they are complete.
