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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.07252 |
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| _version_ | 1866914864545398784 |
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| author | Hinz, Michael Kommer, Jörn |
| author_facet | Hinz, Michael Kommer, Jörn |
| contents | We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$ variables on diagonal neighborhoods to differential $p$-forms. This result generalizes both the well-known classical localization on smooth Riemannian manifolds and the well-known semigroup approximation for quadratic forms. We observe that a related localization map taking functions into forms is well-defined and induces a chain map from a differential complex of Kolmogorov-Alexander-Spanier type onto a differential complex of deRham type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential complexes for local Dirichlet spaces, and non-local-to-local approximations Hinz, Michael Kommer, Jörn Functional Analysis We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$ variables on diagonal neighborhoods to differential $p$-forms. This result generalizes both the well-known classical localization on smooth Riemannian manifolds and the well-known semigroup approximation for quadratic forms. We observe that a related localization map taking functions into forms is well-defined and induces a chain map from a differential complex of Kolmogorov-Alexander-Spanier type onto a differential complex of deRham type. |
| title | Differential complexes for local Dirichlet spaces, and non-local-to-local approximations |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.07252 |