Perturbations of globally hypoelliptic pseudo-differential operators on $\mathbb{R}^n$
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914173076635648 |
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| author | Tokoro, Pedro Meyer |
| author_facet | Tokoro, Pedro Meyer |
| contents | 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 Hörmander classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perturbations of globally hypoelliptic pseudo-differential operators on $\mathbb{R}^n$ Tokoro, Pedro Meyer Analysis of PDEs Primary 35H10, Secondary 35S05 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 Hörmander classes. |
| title | Perturbations of globally hypoelliptic pseudo-differential operators on $\mathbb{R}^n$ |
| topic | Analysis of PDEs Primary 35H10, Secondary 35S05 |
| url | https://arxiv.org/abs/2508.18418 |