"Bottom of the well" semi-classical trace invariants
Abstract
Let 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 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.
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