Denjoy–Carleman solvability of Vekua-type periodic 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.