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A tensor product approach to non-local differential complexes
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Journal Article
A tensor product approach to non-local differential complexes
2024
Overview
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.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
