On a Class of Globally Analytic Hypoelliptic Sums of Squares

TL;DR

This paper investigates certain sums of squares operators on the torus, establishing conditions under which they are globally analytic hypoelliptic, thus advancing understanding of their regularity properties in a global setting.

Contribution

The paper introduces specific assumptions that ensure sums of squares operators on the torus are globally analytic hypoelliptic, excluding cases like the Métivier operator.

Findings

Operators are globally analytic hypoelliptic under certain assumptions.

Excludes the existence of Hamilton leaves along the characteristic variety.

Provides conditions to identify hypoellipticity in global sums of squares operators.

Abstract

We consider sums of squares operators globally defined on the torus. We show that if some assumptions are satisfied the operators are globally analytic hypoelliptic. The purpose of the assumptions is to rule out the existence of a Hamilton leaf on the characteristic variety lying along the fiber of the cotangent bundle, i.e. the case of the (global) M\'etivier operator.