Global hypoellipticity of sums of squares on compact manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866929596457287680 |
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| author | Araújo, Gabriel Ferra, Igor A. Ragognette, Luis F. |
| author_facet | Araújo, Gabriel Ferra, Igor A. Ragognette, Luis F. |
| contents | In this work, we present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on a product of compact Riemannian manifolds $T \times G$, where $G$ is also a Lie group. These new conditions involve the global hypoellipticity of a system of vector fields and are weaker than Hörmander's condition, at the same time that they generalize the well known Diophantine conditions on the torus. We were also able to provide examples of operators satisfying these conditions in the general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_04484 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity of sums of squares on compact manifolds Araújo, Gabriel Ferra, Igor A. Ragognette, Luis F. Analysis of PDEs 35H10 (Primary) 35R01, 35R03 (Secondary) In this work, we present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on a product of compact Riemannian manifolds $T \times G$, where $G$ is also a Lie group. These new conditions involve the global hypoellipticity of a system of vector fields and are weaker than Hörmander's condition, at the same time that they generalize the well known Diophantine conditions on the torus. We were also able to provide examples of operators satisfying these conditions in the general setting. |
| title | Global hypoellipticity of sums of squares on compact manifolds |
| topic | Analysis of PDEs 35H10 (Primary) 35R01, 35R03 (Secondary) |
| url | https://arxiv.org/abs/2005.04484 |