Global hypoellipticity and global solvability of Vekua-type operators associated with diagonal operators on compact Lie groups

TL;DR

This paper investigates the conditions under which Vekua-type operators on compact Lie groups are globally hypoelliptic and solvable, providing characterizations and sufficient conditions for both constant and non-constant coefficient cases.

Contribution

It offers new characterizations of global hypoellipticity and solvability for Vekua-type operators on compact Lie groups, including non-constant coefficient scenarios.

Findings

Characterization of global hypoellipticity for constant coefficient operators

Conditions for global solvability with non-constant coefficients

Sufficient criteria for solvability on classes of Vekua-type operators

Abstract

In this paper, we study Vekua-type operators associated with diagonal operators on compact Lie groups. Characterizations of global hypoellipticity and global solvability properties are presented on classes of Vekua-type operators with constant coefficients. We also present sufficient conditions in order to get global solvability for a class of Vekua-type operators with non-constant coefficients.