Global Gevrey solvability for a class of involutive systems on the torus (Q2039478)

Summary: 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).