ar X iv : m at h / 06 08 61 7 v 1 [ m at h . SP ] 2 4 A ug 2 00 6 “ BOTTOM OF THE WELL ” SEMI - CLASSICAL TRACE INVARIANTS
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چکیده
LetˆH be an-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 ofˆH 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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تاریخ انتشار 2006