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- Title
A tensor product approach to non-local differential complexes.
- Authors
Hinz, Michael; Kommer, Jörn
- 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.
- Subjects
TENSOR products; LAPLACIAN operator; METRIC spaces; HAUSDORFF measures; RIEMANNIAN manifolds; DIFFERENTIAL cross sections
- Publication
Mathematische Annalen, 2024, Vol 389, Issue 3, p2357
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02703-w