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Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields. (English) Zbl 1418.35087
Summary: Let \(L_j = \partial_{tj}+ (a_j + ib_j)(t_j)\partial_x, j=1, \ldots, n,\), be a system of vector fields defined on the torus \(\mathbb{T}^n_t \times \mathbb{T}_x^1\), where the coefficients \(a_j\) and \(b_j\) are real-valued functions belonging to the Gevrey class \(G^s(\mathbb{T}^1), s>1\). The global \(s\)-hypoellipticity of this system is characterized in terms of Diophantine approximations and the Nirenberg-Treves condition (P).

MSC:
35H10 Hypoelliptic equations
35F35 Systems of linear first-order PDEs
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