Distributions in spaces with thick submanifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918168349376512 |
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| author | Ding, Jiajia Vindas, Jasson Yang, Yunyun |
| author_facet | Ding, Jiajia Vindas, Jasson Yang, Yunyun |
| contents | We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test functions may be singular. We define several operations, including ``thick partial derivatives'', and clarify their connection with their classical counterparts in Schwartz distribution theory. We also introduce and study a number of special thick distributions, including new thick delta functions, or more generally thick multilayer distributions along a submanifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_02864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributions in spaces with thick submanifolds Ding, Jiajia Vindas, Jasson Yang, Yunyun Functional Analysis Analysis of PDEs Differential Geometry 46F05, 46F10 We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test functions may be singular. We define several operations, including ``thick partial derivatives'', and clarify their connection with their classical counterparts in Schwartz distribution theory. We also introduce and study a number of special thick distributions, including new thick delta functions, or more generally thick multilayer distributions along a submanifold. |
| title | Distributions in spaces with thick submanifolds |
| topic | Functional Analysis Analysis of PDEs Differential Geometry 46F05, 46F10 |
| url | https://arxiv.org/abs/2408.02864 |