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Contributions of non-extremum critical points to the semi-classical trace formula

Brice Camus
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Abstract

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the trace formula of isolated non-extremum critical points under a condition of "real principal type". The new contribution to the trace formula is valid for all time in a compact subset of $\mathbb{R}$ but the result is modest since we have restrictions on the dimension.

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Brice Camus. 2004-02-28. Contributions of non-extremum critical points to the semi-classical trace formula. https://doi.org/10.1016/j.jfa.2004.02.003

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