Distributions in spaces with thick submanifolds
We have presented 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 defined several op...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024311 |
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| _version_ | 1832590761884909568 |
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| author | Jiajia Ding Jasson Vindas Yunyun Yang |
| author_facet | Jiajia Ding Jasson Vindas Yunyun Yang |
| author_sort | Jiajia Ding |
| collection | DOAJ |
| description | We have presented 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 defined several operations, including 'thick partial derivatives', and clarified their connection with their classical counterparts in Schwartz distribution theory. We also introduced and studied a number of special thick distributions, including new thick delta functions or, more generally, thick multilayer distributions along a submanifold. |
| format | Article |
| id | doaj-art-9a3f0d17bea24b7b9e6ff8c13ebcb960 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-9a3f0d17bea24b7b9e6ff8c13ebcb9602025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126660667910.3934/era.2024311Distributions in spaces with thick submanifoldsJiajia Ding0Jasson Vindas1Yunyun Yang2School of Mathematics, Hefei University of Technology, Hefei 230009, ChinaDepartment of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, 9000 Ghent, BelgiumSchool of Mathematics, Hefei University of Technology, Hefei 230009, ChinaWe have presented 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 defined several operations, including 'thick partial derivatives', and clarified their connection with their classical counterparts in Schwartz distribution theory. We also introduced and studied a number of special thick distributions, including new thick delta functions or, more generally, thick multilayer distributions along a submanifold.https://www.aimspress.com/article/doi/10.3934/era.2024311thick submanifoldsthick delta functionsthick distributionshadamard finite part |
| spellingShingle | Jiajia Ding Jasson Vindas Yunyun Yang Distributions in spaces with thick submanifolds Electronic Research Archive thick submanifolds thick delta functions thick distributions hadamard finite part |
| title | Distributions in spaces with thick submanifolds |
| title_full | Distributions in spaces with thick submanifolds |
| title_fullStr | Distributions in spaces with thick submanifolds |
| title_full_unstemmed | Distributions in spaces with thick submanifolds |
| title_short | Distributions in spaces with thick submanifolds |
| title_sort | distributions in spaces with thick submanifolds |
| topic | thick submanifolds thick delta functions thick distributions hadamard finite part |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024311 |
| work_keys_str_mv | AT jiajiading distributionsinspaceswiththicksubmanifolds AT jassonvindas distributionsinspaceswiththicksubmanifolds AT yunyunyang distributionsinspaceswiththicksubmanifolds |