A tensor product approach to non-local differential complexes

Michael Hinz; Jörn Kommer

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arXiv · 2211.00343

A tensor product approach to non-local differential complexes

Michael Hinz·Jörn Kommer

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Abstract

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.

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BibTeX RIS

Michael Hinz, Jörn Kommer. 2022-11-01. A tensor product approach to non-local differential complexes. https://arxiv.org/abs/2211.00343

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