Spectral determinant for the wave equation on an interval with Dirac damping
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929323261296640 |
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| author | Krejcirik, David Lipovsky, Jiri |
| author_facet | Krejcirik, David Lipovsky, Jiri |
| contents | A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $α$-multiple of the Dirac $δ$-type damping, is derived. Depending on the choice of the branch cut of the logarithm used in its definition, the spectral determinant diverges either for $α=2$ or $α=-2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral determinant for the wave equation on an interval with Dirac damping Krejcirik, David Lipovsky, Jiri Spectral Theory Mathematical Physics Number Theory A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $α$-multiple of the Dirac $δ$-type damping, is derived. Depending on the choice of the branch cut of the logarithm used in its definition, the spectral determinant diverges either for $α=2$ or $α=-2$. |
| title | Spectral determinant for the wave equation on an interval with Dirac damping |
| topic | Spectral Theory Mathematical Physics Number Theory |
| url | https://arxiv.org/abs/2404.11992 |