论文标题
非本地差分配合物的张量产品方法
A tensor product approach to non-local differential complexes
论文作者
论文摘要
我们研究了Kolmogorov-Alexander-Spanier类型的差分复合物在与无界非局部运算符相关的度量空间上，例如分数拉普拉斯类型的操作员。我们定义了希尔伯特综合体，观察不便的特性并获得霍奇拉普拉斯人的自我接触非本地类似物。对于$ d $的定型措施和分数拉普拉斯类型的操作员，我们就可以根据Hausdorff措施提供了可移动集的结果。我们证明了梅耶 - 越野鸟原则和庞加莱引理，并验证在紧凑的里曼尼亚歧管案中，可以回收德勒姆的同胞。
We study differential complexes of Kolmogorov-Alexander-Spanier type on metric measure spaces associated with unbounded non-local operators, such as operators of fractional Laplacian type. We define Hilbert complexes, observe invariance properties and obtain self-adjoint non-local analogues of Hodge Laplacians. For $d$-regular measures and operators of fractional Laplacian type we provide results on removable sets in terms of Hausdorff measures. We prove a Mayer-Vietoris principle and a Poincaré lemma and verify that in the compact Riemannian manifold case the deRham cohomology can be recovered.
