Denjoy-Carleman solvability of Vekua-type periodic operators

TL;DR

This paper investigates the conditions for solvability and hypoellipticity of Vekua-type operators on the torus within Denjoy-Carleman ultradifferentiability, including constant and variable coefficient cases.

Contribution

It provides necessary and sufficient conditions for solvability and hypoellipticity of these operators, extending classical results to ultradifferentiable function spaces.

Findings

Characterized solvability conditions for constant-coefficient operators.

Established criteria for global hypoellipticity in the Denjoy-Carleman setting.

Analyzed solvability for a class of variable coefficient operators.

Abstract

This paper explores the solvability and global hypoellipticity of Vekua-type differential operators on the n-dimensional torus, within the framework of Denjoy-Carleman ultradifferentiability. We provide the necessary and sufficient conditions for achieving these global properties in the case of constant-coefficient operators, along with applications to classical operators. Additionally, we investigate a class of variable coefficients and establish conditions for its solvability.