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.
Denjoy–Carleman solvability of Vekua-type periodic operators
Kirilov, Alexandre;Meyer Tokoro, Pedro
2025-01-01
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.
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