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<p>This paper demonstrates the stability of the global regularity under lower-order perturbations for a class of pseudo-differential operators. 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 hold in the standard Hörmander classes.</p>

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Perturbations of globally hypoelliptic pseudo-differential operators on \({\mathbb {R}}^n\)

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Pedro M. Tokoro

摘要

This paper demonstrates the stability of the global regularity under lower-order perturbations for a class of pseudo-differential operators. 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 hold in the standard Hörmander classes.