Extensions of homogeneous distributions on deformations to the normal cone
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913865074212864 |
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| author | Chamoux, Moudrik |
| author_facet | Chamoux, Moudrik |
| contents | On a deformation to the normal cone $\operatorname{DNC}(M,V)$ we show that given a distribution $u\in\mathcal{D}'(\operatorname{DNC}(M,V)\setminus V\times\mathbb{R})$ if $u$ is homogeneous of order $a$ for the zoom action, then it admits an $a$-homogeneous extension $\widetilde{u}\in\mathcal{D}'(\operatorname{DNC}(M,V))$. We describe all such extensions and discuss briefly about how it translates to the work of Van Erp and Yuncken in arXiv:2303.15787 . The technique used come from the results on the extension of weakly homogeneous distributions provided by Yves Meyer in the 90s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of homogeneous distributions on deformations to the normal cone Chamoux, Moudrik Differential Geometry Functional Analysis On a deformation to the normal cone $\operatorname{DNC}(M,V)$ we show that given a distribution $u\in\mathcal{D}'(\operatorname{DNC}(M,V)\setminus V\times\mathbb{R})$ if $u$ is homogeneous of order $a$ for the zoom action, then it admits an $a$-homogeneous extension $\widetilde{u}\in\mathcal{D}'(\operatorname{DNC}(M,V))$. We describe all such extensions and discuss briefly about how it translates to the work of Van Erp and Yuncken in arXiv:2303.15787 . The technique used come from the results on the extension of weakly homogeneous distributions provided by Yves Meyer in the 90s. |
| title | Extensions of homogeneous distributions on deformations to the normal cone |
| topic | Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2505.22885 |