Generic simplicity of ellipses
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866917727423168512 |
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| author | Hillairet, Luc Judge, Chris M. |
| author_facet | Hillairet, Luc Judge, Chris M. |
| contents | We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the disk (Bourget's hypothesis) and on a refined version of our method of asymptotic separation of variables.
In v1, the statement of prop. 2.1 is correct but the proof is not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic simplicity of ellipses Hillairet, Luc Judge, Chris M. Spectral Theory 35P15 (Primary) 58J50 (Secondary) We prove that the Laplace spectrum of the generic ellipse is simple, both with Neumann and Dirichlet boundary condition. We rely on the known multiplicities in the spectrum of the disk (Bourget's hypothesis) and on a refined version of our method of asymptotic separation of variables. In v1, the statement of prop. 2.1 is correct but the proof is not. |
| title | Generic simplicity of ellipses |
| topic | Spectral Theory 35P15 (Primary) 58J50 (Secondary) |
| url | https://arxiv.org/abs/2403.07377 |