On some quasianalytic classes of $C^\infty$ functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915089166106624 |
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| author | Elkhadiri, Abdelhafed |
| author_facet | Elkhadiri, Abdelhafed |
| contents | This expository article is devoted to the notion of quasianalytic classes and the Borel mapping. Although quasianalytic classes are well known in analysis since several decades. We are interested in certain properties of Denjoy-Carleman's quasianalytic classes, such as the non-surjectivity of the Borel mapping, the property of monotonicity. We try to see if it remains true for other quasianalytic classes, such as for example, the classes of indefinitely differentiable functions definable in a polynomially bounded o-minimal structures. What motivated this is the fact of having shown in a previous article the existence of quasianalytic classes where Borel mapping is surjective. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some quasianalytic classes of $C^\infty$ functions Elkhadiri, Abdelhafed Classical Analysis and ODEs Analysis of PDEs 26E10, 58C25, 46E25 This expository article is devoted to the notion of quasianalytic classes and the Borel mapping. Although quasianalytic classes are well known in analysis since several decades. We are interested in certain properties of Denjoy-Carleman's quasianalytic classes, such as the non-surjectivity of the Borel mapping, the property of monotonicity. We try to see if it remains true for other quasianalytic classes, such as for example, the classes of indefinitely differentiable functions definable in a polynomially bounded o-minimal structures. What motivated this is the fact of having shown in a previous article the existence of quasianalytic classes where Borel mapping is surjective. |
| title | On some quasianalytic classes of $C^\infty$ functions |
| topic | Classical Analysis and ODEs Analysis of PDEs 26E10, 58C25, 46E25 |
| url | https://arxiv.org/abs/2501.01479 |