标题： 全局超椭圆伪微分算子在$\mathbb{R}^n$上的扰动 显示英文标题

标题： Perturbations of globally hypoelliptic pseudo-differential operators on $\mathbb{R}^n$

摘要： 本文展示了在低阶扰动下，一类伪微分算子的全局正则性的稳定性。 我们证明了如果一个算子具有全局拟椭圆符号，当其被足够低阶的算子扰动时，其全局正则性（在Schwartz函数和缓增分布的意义下）得以保持。 该结果特别适用于Shubin和SG类中的算子。 此外，我们讨论了为什么这一稳定性结果不适用于标准的Hörmander类。 显示英文摘要

摘要： This paper demonstrates the stability of the global regularity for a class of pseudo-differential operators under lower-order perturbations. We establish that if an operator has a globally hypoelliptic symbol, its global regularity (in the sense of Schwartz functions and tempered distributions) is preserved when perturbed by operators of sufficiently lower order. This result applies in particular to operators within the Shubin and SG classes. Furthermore, we discuss why this stability result does not hold in the standard H\"ormander classes.