The Baouendi-Treves approximation Theorem for Gevrey classes and applications

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 Poincaré Lemma and study ultradistributions vanishing on maximally real submanifolds. Contents 1. Introduction 1 2. Definitions and Preliminar Results 3 3. The ultradifferentiable Baouendi-Treves approximation formula 4 4. Approximate Poincaré Lemma 12 5. Ultradistributions vanishing on maximally real submanifolds 14 6. Baouendi-Treves theorem in Denjoy-Carleman classes 15 Appendix A. Faà di Bruno formula 15 Appendix B. Trace of ultradistributions 17 References 19