The Hahn-Banach theorem in spaces of nonlinear generalized functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912069131960320 |
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| author | Kebiche, Djamel eddine Giordano, Paolo |
| author_facet | Kebiche, Djamel eddine Giordano, Paolo |
| contents | In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our approach addresses the case where maps are defined $\varepsilon$-wise, which simplifies the framework and makes the extension of linear functionals more manageable. As an application of our main result, we demonstrate the separation of convex sets in Colombeau spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hahn-Banach theorem in spaces of nonlinear generalized functions Kebiche, Djamel eddine Giordano, Paolo Functional Analysis In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our approach addresses the case where maps are defined $\varepsilon$-wise, which simplifies the framework and makes the extension of linear functionals more manageable. As an application of our main result, we demonstrate the separation of convex sets in Colombeau spaces. |
| title | The Hahn-Banach theorem in spaces of nonlinear generalized functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.08679 |