Solvability of a class of evolution operators on compact Lie groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918342626902016 |
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| author | Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| author_facet | Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer |
| contents | This paper provides sufficient conditions for the solvability of a class of first-order evolution operators of Vekua-type on the product of a one-dimensional torus and a compact Lie group. The conditions are expressed in terms of the time-dependent coefficients and the spectral behavior of a normalized left-invariant vector field on the group. The three-sphere case is discussed in detail, leading to more explicit criteria, and the main results are further extended to operators defined on finite products of compact Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15203 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvability of a class of evolution operators on compact Lie groups Kirilov, Alexandre de Moraes, Wagner Augusto Almeida Tokoro, Pedro Meyer Analysis of PDEs Primary 35A01, 35B10, Secondary 35F15, 43A75, 22E30 This paper provides sufficient conditions for the solvability of a class of first-order evolution operators of Vekua-type on the product of a one-dimensional torus and a compact Lie group. The conditions are expressed in terms of the time-dependent coefficients and the spectral behavior of a normalized left-invariant vector field on the group. The three-sphere case is discussed in detail, leading to more explicit criteria, and the main results are further extended to operators defined on finite products of compact Lie groups. |
| title | Solvability of a class of evolution operators on compact Lie groups |
| topic | Analysis of PDEs Primary 35A01, 35B10, Secondary 35F15, 43A75, 22E30 |
| url | https://arxiv.org/abs/2602.15203 |