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<p>We consider a complex of pseudo-differential operators associated with an overdetermined system of operators defined on the torus. We characterize the global solvability of this complex when the system has constant coefficients. Furthermore, for a class with time-dependent coefficients, we establish connections between the global solvability of the complex and the global solvability of its normal form, namely, a suitable system with constant coefficients.</p>

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Globally solvable complexes of pseudo-differential operators on the torus

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Fernando de Ávila Silva,
  • Cleber de Medeira

摘要

We consider a complex of pseudo-differential operators associated with an overdetermined system of operators defined on the torus. We characterize the global solvability of this complex when the system has constant coefficients. Furthermore, for a class with time-dependent coefficients, we establish connections between the global solvability of the complex and the global solvability of its normal form, namely, a suitable system with constant coefficients.