"Bottom of the well" semi-classical trace invariants

Guillemin, V.; Paul, T.; Uribe, A.

"Bottom of the well" semi-classical trace invariants

Authors

Guillemin, V.

Paul, T.

Uribe, A.

Description

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.
9 pages