ANALYTIC MICROLOCAL BOHR-SOMMERFELD EXPANSIONS - Centre Henri Lebesgue
Pré-Publication, Document De Travail Année : 2025

ANALYTIC MICROLOCAL BOHR-SOMMERFELD EXPANSIONS

Résumé

This article is devoted to Gevrey-analytic estimates in ℏ, of the Bohr-Sommerfeld expansion of the eigenvalues of self-adjoint pseudo-differential 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 πℏ in the Bargmann space.
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Dates et versions

hal-04871673 , version 1 (07-01-2025)

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  • HAL Id : hal-04871673 , version 1

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Antide Duraffour. ANALYTIC MICROLOCAL BOHR-SOMMERFELD EXPANSIONS. 2025. ⟨hal-04871673⟩
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