"Bottom of the well" semi-classical trace invariants

• Autores: Victor Guillemin, T. Paul, Alejandro Uribe
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 4, 2007, págs. 711-719
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n4.a16
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let $\hat H$ be an $\h$-admissible pseudodifferential operator whose principal symbol, $H$, has a unique non-degenerate global minimum. We give a simple proof that the semi-classical asymptotics of the eigenvalues of $\hat H$ corresponding to the ``bottom of the well" determine the Birkhoff normal form of $H$ at the minimum. We treat both the resonant and the non-resonant cases.