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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/2408.06835 |
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| _version_ | 1866914911430377472 |
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| author | Zeng, Chunna Lan, Yu |
| author_facet | Zeng, Chunna Lan, Yu |
| contents | A complete classification is established for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx). The assumption of matrix symmetry is eliminated. For n>2, such valuation is uniquely characterized by the moment matrix of measurable function. In the 2-dimensional case, while the rotation matrix shows up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SL(n) covariant matrix-valued valuations on Lp-spaces Zeng, Chunna Lan, Yu Differential Geometry A complete classification is established for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx). The assumption of matrix symmetry is eliminated. For n>2, such valuation is uniquely characterized by the moment matrix of measurable function. In the 2-dimensional case, while the rotation matrix shows up. |
| title | SL(n) covariant matrix-valued valuations on Lp-spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.06835 |