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.
Domaines
Théorie spectrale [math.SP]Origine | Fichiers produits par l'(les) auteur(s) |
---|