Let $L_j={\partial}/{\partial t_j}+(a_j+ib_j)(t_j){\partial}/{\partial x}$, $j=1,\ldots,n$, be a system of complex vector fields defined on the $(n+1)$-dimensional torus, where $a_j$ and $b_j$ are real-valued functions belonging to the Gevrey class $ G^s(\mathbb{T}^1)$, $s > 1$. We present a complete characterization to the global $s$-solvability of this system in terms of diophantine properties of the coefficients and the Nirenberg–Treves condition (P).

中文翻译：

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环面上一类对合系统的全局 Gevrey 可解性

令 $L_j={\partial}/{\partial t_j}+(a_j+ib_j)(t_j){\partial}/{\partial x}$, $j=1,\ldots,n$, 是一个系统在 $(n+1)$ 维环面上定义的复向量场，其中 $a_j$ 和 $b_j$ 是属于 Gevrey 类 $G^s(\mathbb{T}^1)$ 的实值函数， $s > 1$。我们根据系数的丢番图性质和 Nirenberg-Treves 条件 (P) 对该系统的全局 $s$-可解性进行了完整的表征。