Differentiability Properties of Log-Analytic Functions

TL;DR

This paper investigates the differentiability and quasianalytic properties of log-analytic functions, establishing that their derivatives are also log-analytic and proving a parametric version of Tamm's theorem.

Contribution

It demonstrates that derivatives of log-analytic functions remain log-analytic and proves a parametric Tamm's theorem for these functions, advancing understanding of their structural properties.

Findings

Derivative of a log-analytic function is log-analytic

Log-analytic functions are strongly quasianalytic

Parametric Tamm's theorem holds for log-analytic functions

Abstract

We show that the derivative of a log-analytic function is log-analytic. We prove that log-analytic functions exhibit strong quasianalytic properties. We establish the parametric version of Tamm's theorem for log-analytic functions.