Counter-examples to the fractal Weyl law for semiclassical resonances
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918229857796096 |
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| author | Bony, Jean-Francois Fujiie, Setsuro Ramond, Thierry Zerzeri, Maher |
| author_facet | Bony, Jean-Francois Fujiie, Setsuro Ramond, Thierry Zerzeri, Maher |
| contents | Under general assumptions, the numbers of semiclassical resonances is known to be bounded from above by a negative power of $h$ which is given by the fractal dimension of the trapped set. In this paper we provide examples of operators with much less resonances, showing that these upper bounds are not always sharp. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counter-examples to the fractal Weyl law for semiclassical resonances Bony, Jean-Francois Fujiie, Setsuro Ramond, Thierry Zerzeri, Maher Analysis of PDEs Mathematical Physics Spectral Theory 35B34, 81Q20, 81U24, 37C29, 35J10, 35P20 Under general assumptions, the numbers of semiclassical resonances is known to be bounded from above by a negative power of $h$ which is given by the fractal dimension of the trapped set. In this paper we provide examples of operators with much less resonances, showing that these upper bounds are not always sharp. |
| title | Counter-examples to the fractal Weyl law for semiclassical resonances |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory 35B34, 81Q20, 81U24, 37C29, 35J10, 35P20 |
| url | https://arxiv.org/abs/2512.03773 |