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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06046 |
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| _version_ | 1866911716964564992 |
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| author | Duraffour, Antide |
| author_facet | Duraffour, Antide |
| contents | This article is devoted to analytic (in the sense of Boutet de Monvel-Sjöstrand) estimates in $\hbar$, of the Bohr-Sommerfeld expansion of the eigenvalues of self-adjoint pseudodifferential operators acting on $L^2(R)$ in the regular case. We consider an interval of energies in which the spectrum of P is discrete and such that the energy sets are regular connected curves. Under some assumptions on the holomorphy of the symbol p, we will use the isometry between $L^2(R)$ and the Bargmann space to obtain an exponentially sharp description of the spectrum in the energy window . More precisely it is possible to build exponentially sharp WKB quasimodes in the Bargmann space. A precise examination of the principal symbols will provide an interpretation to the Maslov correction $π\hbar$ in the Bargmann space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Microlocal Bohr-Sommerfeld Expansions Duraffour, Antide Spectral Theory This article is devoted to analytic (in the sense of Boutet de Monvel-Sjöstrand) estimates in $\hbar$, of the Bohr-Sommerfeld expansion of the eigenvalues of self-adjoint pseudodifferential operators acting on $L^2(R)$ in the regular case. We consider an interval of energies in which the spectrum of P is discrete and such that the energy sets are regular connected curves. Under some assumptions on the holomorphy of the symbol p, we will use the isometry between $L^2(R)$ and the Bargmann space to obtain an exponentially sharp description of the spectrum in the energy window . More precisely it is possible to build exponentially sharp WKB quasimodes in the Bargmann space. A precise examination of the principal symbols will provide an interpretation to the Maslov correction $π\hbar$ in the Bargmann space. |
| title | Analytic Microlocal Bohr-Sommerfeld Expansions |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2501.06046 |