A class of globally analytic hypoelliptic operators on compact Lie groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909157315051520 |
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| author | Jahnke, Max Reinhold Rodrigues, Nicholas Braun |
| author_facet | Jahnke, Max Reinhold Rodrigues, Nicholas Braun |
| contents | We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key conditions are: the vector fields must satisfy Hörmander's finite type condition; there exists a closed subgroup whose action leaves the vector fields invariant; and the operator must be elliptic in directions transversal to the action of the subgroup. This paves the way for further studies on the regularity of sums of squares on principal fiber bundles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A class of globally analytic hypoelliptic operators on compact Lie groups Jahnke, Max Reinhold Rodrigues, Nicholas Braun Analysis of PDEs We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as a zero-order perturbation of a sum of squares of vector fields with real-analytic coefficients on compact Lie groups. The key conditions are: the vector fields must satisfy Hörmander's finite type condition; there exists a closed subgroup whose action leaves the vector fields invariant; and the operator must be elliptic in directions transversal to the action of the subgroup. This paves the way for further studies on the regularity of sums of squares on principal fiber bundles. |
| title | A class of globally analytic hypoelliptic operators on compact Lie groups |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.01772 |