论文标题
在（全球）分数离散laplacian的独特延续属性
On (Global) Unique Continuation Properties of the Fractional Discrete Laplacian
论文作者
论文摘要
我们研究了分数离散的拉普拉斯式的各种定性和定量（全球）独特的延续性能。我们表明，虽然分数拉普拉斯人以（全球）独特的延续属性的形式享有惊人的刚性属性，但总体上不喜欢分数离散的laplacian。虽然离散化可以抵消连续分数拉普拉斯式的强刚性特性，但通过讨论唯一延续的定量形式，我们说明，如果添加了指数较小（晶格大小）校正项，则可以恢复这些特性。这特别使我们能够针对分数拉普拉斯式的离散线性反问题推断出统一的稳定性。我们以转移原则以及对离散曲线的这些特性的讨论对这些观察结果进行了补充。
We study various qualitative and quantitative (global) unique continuation properties for the fractional discrete Laplacian. We show that while the fractional Laplacian enjoys striking rigidity properties in the form of (global) unique continuation properties, the fractional discrete Laplacian does not enjoy these in general. While discretization thus counteracts the strong rigidity properties of the continuum fractional Laplacian, by discussing quantitative forms of unique continuation, we illustrate that these properties can be recovered if exponentially small (in the lattice size) correction terms are added. This in particular allows us to deduce uniform stability properties for a discrete, linear inverse problem for the fractional Laplacian. We complement these observations with a transference principle and the discussion of these properties on the discrete torus.
