Restricted log-exp-analytic power functions
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 57-78
MSC: Primary 03C64; Secondary 26A09, 26E05, 26E10.
DOI: 10.4064/ap221218-2-6
Published online: 28 July 2023
Abstract
A preparation theorem for compositions of restricted log-exp-analytic functions and power functions of the form $$ h: \mathbb R \to \mathbb R,\quad x \mapsto \bigg \{\begin {array}{@{}ll@{}} x^r, & x \gt 0, \\ 0, & \text{else}, \end {array} $$ for $r \in \mathbb R$ is given. Consequently, a parametric version of Tamm’s theorem for this class of functions is obtained which is indeed a full generalization of the parametric version of Tamm’s theorem for $\mathbb R_{\rm an}^{\mathbb R}$-definable functions.
