Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2501.06046 |
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Sommario:
- 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.