Generalized functions with infinitesimals
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912659235930112 |
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| author | Vernaeve, Hans |
| author_facet | Vernaeve, Hans |
| contents | We give a survey of the use of infinitesimals within mathematical analysis to rigorously deal with the delta-function from physics, and more generally, with distributions in the sense of L. Schwartz. We use the framework of nonstandard analysis as introduced by A. Robinson to rigorously deal with infinitesimals. Our exposition tries to be elementary, except for familiarity with nonstandard analysis, and takes as a starting point one of the basic questions in PDE for which distribution theory was developed. No knowledge of distribution theory is required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized functions with infinitesimals Vernaeve, Hans Functional Analysis Logic 26E35, 46F05, 46S20 We give a survey of the use of infinitesimals within mathematical analysis to rigorously deal with the delta-function from physics, and more generally, with distributions in the sense of L. Schwartz. We use the framework of nonstandard analysis as introduced by A. Robinson to rigorously deal with infinitesimals. Our exposition tries to be elementary, except for familiarity with nonstandard analysis, and takes as a starting point one of the basic questions in PDE for which distribution theory was developed. No knowledge of distribution theory is required. |
| title | Generalized functions with infinitesimals |
| topic | Functional Analysis Logic 26E35, 46F05, 46S20 |
| url | https://arxiv.org/abs/2510.16484 |