We introduce a new class of ultradifferentiable pseudodifferential operators on the torus whose calculus allows us to show that global hypoellipticity, in ultradifferentiable classes, with a finite loss of derivatives of a system of pseudodifferential operators, is stable under perturbations by lower order pseudodifferential operators whose order depends on the loss of derivatives. The key point in our study is our definition of loss of derivatives. We also give an easy proof of the fact that if a system of pseudodifferential operators is globally \({\mathcal {M}}\)-hypoelliptic then its transpose is globally solvable in \(D'_{\mathcal {M}}\left( {\mathbb {T}}^N\right) \). Finally we present an application of our results.

我们在圆环上引入了一类新的超微分伪微分算子，其微积分使我们能够证明，在微分类中的全局次椭圆性在伪微分算子系统的导数有限的损失下，在低阶伪微分算子的扰动下是稳定的。取决于衍生品的损失。我们研究的重点是我们对衍生工具损失的定义。我们还简单地证明了以下事实：如果伪微分算子系统是全局\（{\ mathcal {M}} \）-次椭圆形，那么其转置就可以在\（D'_ {\ mathcal {M}}中全局求解\ left（{\ mathbb {T}} ^ N \ right）\）。最后，我们介绍了我们的结果。