Multiplicative convolution with symmetries in Euclidean space and on the sphere
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913725614653440 |
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| author | Nagel, Felix |
| author_facet | Nagel, Felix |
| contents | Multiplicative convolution $μ\ast ν$ of two finite signed measures $μ$ and $ν$ on $\mathbb{R}^n$ and a related product $μ\circledast ν$ on the sphere $S^{n-1}$ are studied. For fixed $μ$ the injectivity in $ν$ of both operations is characterised given an arbitrary group of reflections along the coordinate axes. The results for the sphere yield generalised versions of the theorems in Molchanov and Nagel (2021) about convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicative convolution with symmetries in Euclidean space and on the sphere Nagel, Felix Probability Functional Analysis Metric Geometry 28A99, 44A35, 52A22 Multiplicative convolution $μ\ast ν$ of two finite signed measures $μ$ and $ν$ on $\mathbb{R}^n$ and a related product $μ\circledast ν$ on the sphere $S^{n-1}$ are studied. For fixed $μ$ the injectivity in $ν$ of both operations is characterised given an arbitrary group of reflections along the coordinate axes. The results for the sphere yield generalised versions of the theorems in Molchanov and Nagel (2021) about convex bodies. |
| title | Multiplicative convolution with symmetries in Euclidean space and on the sphere |
| topic | Probability Functional Analysis Metric Geometry 28A99, 44A35, 52A22 |
| url | https://arxiv.org/abs/2503.06180 |