Global properties of vector fields on compact Lie groups in Komatsu classes

TL;DR

This paper characterizes the global hypoellipticity and solvability of constant-coefficient vector fields on compact Lie groups within Komatsu classes, examining how perturbations affect these properties.

Contribution

It provides a complete characterization of hypoellipticity and solvability for such vector fields in Komatsu classes, including the impact of lower order perturbations.

Findings

Complete characterization of hypoellipticity and solvability in Komatsu classes.

Analysis of perturbation effects on these properties.

Results applicable to both Roumieu and Beurling types.

Abstract

In this paper we characterize completely the global hypoellipticity and global solvability in the sense of Komatsu (of Roumieu and Beurling types) of constant-coefficients vector fields on compact Lie groups. We also analyze the influence of perturbations by lower order terms in the preservation of these properties.