Restricted log-exp-analytic functions and some differentiability results

Abstract

In this article, we define restricted log-exp-analytic functions as compositions of log-analytic functions and exponentials of locally bounded functions. We prove that the derivative of a restricted log-exp-analytic function is again restricted log-exp-analytic and that such a function exhibits strong quasianalytic properties. We establish the parametric version of Tamm’s theorem for this class of functions.