The Theorem of Iterates for elliptic and non-elliptic Operators

TL;DR

This paper develops a new ultradifferentiable framework to analyze the Problem of Iterates, extending previous results to non-elliptic operators and broadening the scope of hypoelliptic operator analysis.

Contribution

It introduces a generalized approach for the Problem of Iterates using ultradifferentiable structures, enabling non-analytic theorems for non-elliptic differential operators.

Findings

Proves non-analytic Theorems of Iterates for non-elliptic operators.

Extends the Theorem of Baouendi and Metivier to hypoelliptic operators.

Generalizes previous settings including the Gevrey case.

Abstract

We introduce a new approach for the study of the Problem of Iterates using the theory on general ultradifferentiable structures developed in the last years. Our framework generalizes many of the previous settings including the Gevrey case and enables us, for the first time, to prove non-analytic Theorems of Iterates for non-elliptic differential operators. In particular, by generalizing a Theorem of Baouendi and Metivier we obtain the Theorem of Iterates for hypoelliptic analytic operators of principal type with respect to several non-analytic ultradifferentiable structures.