Restricted Log-Exp-Analytic Power Functions

Autor:	Opris, Andre
Rok vydání:	2022
Předmět:	Mathematics - Logic Mathematics - Algebraic Geometry Mathematics - Classical Analysis and ODEs 03C64 14P15 26A09 26E05 26E10 32B20 F.4.1
Druh dokumentu:	Working Paper
Popis:	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. Comment: arXiv admin note: substantial text overlap with arXiv:2112.10818, arXiv:2205.12011, arXiv:2112.08161
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.09141 Zobrazit plný text záznamu View this record from Arxiv