Uniform extension of definable $C^{m,ω}$-Whitney jets
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909317957943296 |
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| author | Parusiński, Adam Rainer, Armin |
| author_facet | Parusiński, Adam Rainer, Armin |
| contents | We show that definable Whitney jets of class $C^{m,ω}$, where $m$ is a nonnegative integer and $ω$ is a modulus of continuity, are the restrictions of definable $C^{m,ω}$-functions; "definable" refers to an arbitrary given o-minimal expansion of the real field. This is true in a uniform way: any definable bounded family of Whitney jets of class $C^{m,ω}$ extends to a definable bounded family of $C^{m,ω}$-functions. We also discuss a uniform $C^m$-version and how the extension depends on the modulus of continuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform extension of definable $C^{m,ω}$-Whitney jets Parusiński, Adam Rainer, Armin Logic Algebraic Geometry Classical Analysis and ODEs Functional Analysis We show that definable Whitney jets of class $C^{m,ω}$, where $m$ is a nonnegative integer and $ω$ is a modulus of continuity, are the restrictions of definable $C^{m,ω}$-functions; "definable" refers to an arbitrary given o-minimal expansion of the real field. This is true in a uniform way: any definable bounded family of Whitney jets of class $C^{m,ω}$ extends to a definable bounded family of $C^{m,ω}$-functions. We also discuss a uniform $C^m$-version and how the extension depends on the modulus of continuity. |
| title | Uniform extension of definable $C^{m,ω}$-Whitney jets |
| topic | Logic Algebraic Geometry Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2306.09156 |