Contents Online
Mathematical Research Letters
Volume 14 (2007)
Number 4
“Bottom of the well” semi-classical trace invariants
Pages: 711 – 719
DOI: https://dx.doi.org/10.4310/MRL.2007.v14.n4.a16
Authors
Abstract
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.
Published 1 January 2007