The Baouendi-Treves approximation Theorem for Gevrey classes and applications

TL;DR

This paper extends the Baouendi-Treves approximation theorem to Gevrey classes and ultradistributions, providing new tools for analysis and applications in complex analysis and distribution theory.

Contribution

It introduces a Gevrey version of the approximation theorem and explores applications like the approximate Poincaré Lemma and ultradistributions vanishing on real submanifolds.

Findings

Extended the approximation theorem to Gevrey functions and ultradistributions

Developed a Gevrey version of the approximate Poincaré Lemma

Analyzed ultradistributions vanishing on maximally real submanifolds

Abstract

In this work we show how to extend the seminal Baouendi-Treves approximation theorem for Gevrey functions and ultradistributions. As applications we present a Gevrey version of the approximate Poincar\'e Lemma and study ultradistributions vanishing on maximally real submanifolds.