"Bottom of the well" semi-classical trace invariants

Details "Bottom of the well" semi-classical trace invariants "Bottom of the well" semi-classical trace invariants

2006-08-24

arxiv.org/abs/math/0608617v1

Mathematics

Spectral Theory

9 pages

Scientific paper

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.

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