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

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

2004-02-28

arxiv.org/abs/math/0403007v1

Journal of Functional Analysis, Volume 217, Issue 1 , 1 December 2004, Pages 79-102

Mathematics

Functional Analysis

24 pages

Scientific paper

10.1016/j.jfa.2004.02.003

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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