Restricted Log-Exp-Analytic Power Functions
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909654694494208 |
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| author | Opris, Andre |
| author_facet | Opris, Andre |
| contents | A preparation theorem for compositions of restricted log-exp-analytic functions and power functions of the form $$h: \mathbb{R} \to \mathbb{R}, x \mapsto \left\{\begin{array}{ll} x^r, & x > 0, \\ 0, & \textnormal{ else, } \end{array}\right.$$ for $r \in \mathbb{R}$ is given. Consequently we obtain a parametric version of Tamm's theorem for this class of functions which is indeed a full generalisation of the parametric version of Tamm's theorem for $\mathbb{R}_{\textnormal{an}}^{\mathbb{R}}$-definable functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09141 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Restricted Log-Exp-Analytic Power Functions Opris, Andre Logic Algebraic Geometry Classical Analysis and ODEs 03C64, 14P15, 26A09, 26E05, 26E10, 32B20 F.4.1 A preparation theorem for compositions of restricted log-exp-analytic functions and power functions of the form $$h: \mathbb{R} \to \mathbb{R}, x \mapsto \left\{\begin{array}{ll} x^r, & x > 0, \\ 0, & \textnormal{ else, } \end{array}\right.$$ for $r \in \mathbb{R}$ is given. Consequently we obtain a parametric version of Tamm's theorem for this class of functions which is indeed a full generalisation of the parametric version of Tamm's theorem for $\mathbb{R}_{\textnormal{an}}^{\mathbb{R}}$-definable functions. |
| title | Restricted Log-Exp-Analytic Power Functions |
| topic | Logic Algebraic Geometry Classical Analysis and ODEs 03C64, 14P15, 26A09, 26E05, 26E10, 32B20 F.4.1 |
| url | https://arxiv.org/abs/2212.09141 |