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In this note, we explore global properties for systems of first-order differential operators, with a focus on zero-order perturbations of constant-coefficient vector fields defined on products of tori and three-dimensional spheres. By analyzing the behavior of the symbol of the system, we establish necessary and sufficient conditions for achieving global hypoellipticity, global analytic hypoellipticity and global solvability.

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Diophantine Conditions and Global Properties for Systems of Vector Fields in Tori and Spheres

  • 会议论文

  • 发表日期：

    2025年

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  • Alexandre Kirilov,
  • Ricardo Paleari da Silva

摘要

In this note, we explore global properties for systems of first-order differential operators, with a focus on zero-order perturbations of constant-coefficient vector fields defined on products of tori and three-dimensional spheres. By analyzing the behavior of the symbol of the system, we establish necessary and sufficient conditions for achieving global hypoellipticity, global analytic hypoellipticity and global solvability.