A groupoid approach to the Wodzicki residue and the Kontsevich-Vishik trace
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913489544544256 |
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| author | Mohsen, Omar |
| author_facet | Mohsen, Omar |
| contents | Building on the work of Debord and Skandalis, van Erp and Yuncken introduced a groupoid approach to pseudo-differential operators which has various advantages over the classical approach using Hörmander's symbolic calculus. In a recent work by Couchet and Yuncken, they showed that for pseudo-differential operators of order $-\dim(M)$ acting on a smooth manifold $M$ the Wodzicki residue can be naturally obtained from van Erp and Yuncken's approach. In this short note, we extend their work to pseudo-differential operators of any order. We also give a description of the Kontsevich-Vishik trace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10415 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A groupoid approach to the Wodzicki residue and the Kontsevich-Vishik trace Mohsen, Omar Analysis of PDEs Differential Geometry Operator Algebras Building on the work of Debord and Skandalis, van Erp and Yuncken introduced a groupoid approach to pseudo-differential operators which has various advantages over the classical approach using Hörmander's symbolic calculus. In a recent work by Couchet and Yuncken, they showed that for pseudo-differential operators of order $-\dim(M)$ acting on a smooth manifold $M$ the Wodzicki residue can be naturally obtained from van Erp and Yuncken's approach. In this short note, we extend their work to pseudo-differential operators of any order. We also give a description of the Kontsevich-Vishik trace. |
| title | A groupoid approach to the Wodzicki residue and the Kontsevich-Vishik trace |
| topic | Analysis of PDEs Differential Geometry Operator Algebras |
| url | https://arxiv.org/abs/2312.10415 |