Computability of a Whitney Extension
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918426889420800 |
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| author | Brun, Andrea Gherardi, Guido Marcone, Alberto |
| author_facet | Brun, Andrea Gherardi, Guido Marcone, Alberto |
| contents | We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if $F \subseteq \mathbb{R}^n$ is a closed set represented so that the distance function $x \mapsto d(x,F)$ can be computed, and $(f^{(\bar{k})})_{|\bar{k}| \le m}$ is a Whitney jet of order $m$ on $F$, then we can compute $g \in C^{m}(\mathbb{R}^n)$ such that $g$ and its partial derivatives coincide on $F$ with the corresponding functions of $(f^{(\bar{k})})_{|\bar{k}| \le m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computability of a Whitney Extension Brun, Andrea Gherardi, Guido Marcone, Alberto Logic Classical Analysis and ODEs 03D78, 26E10, 58C25, 54C20, 54C30 We prove the computability of a version of Whitney Extension, when the input is suitably represented. More specifically, if $F \subseteq \mathbb{R}^n$ is a closed set represented so that the distance function $x \mapsto d(x,F)$ can be computed, and $(f^{(\bar{k})})_{|\bar{k}| \le m}$ is a Whitney jet of order $m$ on $F$, then we can compute $g \in C^{m}(\mathbb{R}^n)$ such that $g$ and its partial derivatives coincide on $F$ with the corresponding functions of $(f^{(\bar{k})})_{|\bar{k}| \le m}$. |
| title | Computability of a Whitney Extension |
| topic | Logic Classical Analysis and ODEs 03D78, 26E10, 58C25, 54C20, 54C30 |
| url | https://arxiv.org/abs/2507.02113 |