This article studies the global hypoellipticity of a class of overdetermined systems of pseudo-differential operators defined on the torus. The main goal consists in establishing connections between the global hypoellipticity of the system and the global hypoellipticity of its normal form. It is proved that an obstruction of number-theoretical nature appears as a necessary condition to the global hypoellipticity. Conversely, the sufficiency is approached by analyzing three types of hypotheses: a Hörmander condition, logarithmic growth and super-logarithmic growth.

中文翻译：

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一类超确定的环上伪微分算子的全局次椭圆性

本文研究了在圆环上定义的一类超定拟伪微分算子系统的全局次椭圆性。主要目标在于在系统的整体次椭圆率与其正常形式的整体次椭圆率之间建立联系。事实证明，数论性质的障碍是整体次椭圆性的必要条件。相反，通过分析三种类型的假设可以得出充分性：Hörmander条件，对数增长和超对数增长。