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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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##### References:
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