Boundary spectral estimates for semiclassical Gevrey operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914914989244416 |
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| author | Xiong, Haoren |
| author_facet | Xiong, Haoren |
| contents | We obtain the spectral and resolvent estimates for semiclassical pseudodifferential operators with symbol of Gevrey-$s$ regularity, near the boundary of the range of the principal symbol. We prove that the boundary spectrum free region is of size ${\mathcal O}(h^{1-\frac{1}{s}})$ where the resolvent is at most fractional exponentially large in $h$, as the semiclassical parameter $h\to 0^+$. This is a natural Gevrey analogue of a result by N. Dencker, J. Sj{ö}strand, and M. Zworski in the $C^{\infty}$ and analytic cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary spectral estimates for semiclassical Gevrey operators Xiong, Haoren Spectral Theory Analysis of PDEs Complex Variables We obtain the spectral and resolvent estimates for semiclassical pseudodifferential operators with symbol of Gevrey-$s$ regularity, near the boundary of the range of the principal symbol. We prove that the boundary spectrum free region is of size ${\mathcal O}(h^{1-\frac{1}{s}})$ where the resolvent is at most fractional exponentially large in $h$, as the semiclassical parameter $h\to 0^+$. This is a natural Gevrey analogue of a result by N. Dencker, J. Sj{ö}strand, and M. Zworski in the $C^{\infty}$ and analytic cases. |
| title | Boundary spectral estimates for semiclassical Gevrey operators |
| topic | Spectral Theory Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2408.09098 |