Restricted Log-Exp-Analytic Functions and some Differentiability Results

TL;DR

This paper introduces restricted log-exp-analytic functions, demonstrating their closure under differentiation, quasianalytic properties, and establishing a parametric version of Tamm's theorem for this class.

Contribution

It defines a new class of functions and proves their closure properties, quasianalyticity, and a parametric Tamm's theorem, advancing the understanding of their differentiability and structure.

Findings

Derivative of restricted log-exp-analytic functions remains in the class

These functions exhibit strong quasianalytic properties

A parametric version of Tamm's theorem is established for them

Abstract

In this article we define restricted log-exp-analytic functions as compositions of log-analytic functions and exponentials whose logarithm are locally bounded. 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.