Global Complexification of Real Analytic Restricted Log-Exp-Analytic Functions

TL;DR

This paper proves that real analytic restricted log-exp-analytic functions can be extended holomorphically while preserving their class, including a parametric version of this extension.

Contribution

It introduces a method to holomorphically extend restricted log-exp-analytic functions without leaving their class, including parametric cases.

Findings

Holomorphic extension preserves the restricted log-exp-analytic class

Extension results apply uniformly in parameters

Provides a new tool for complexification of real analytic functions

Abstract

We show that a real analytic restricted log-exp-analytic function has a holomorphic extension which is again restricted log-exp-analytic. We also establish a parametric version of this result.