A semi-classical trace formula at a totally degenerate critical level

Abstract

We study the semi-classical trace formula at a critical energy level for an $h$-pseudo-differential operator on ${\mathbb{R}}^n$ whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a large time behavior and under the hypothesis that the principal symbol of the operator has a local extremum at the critical point.

15 pages

References in corpus (1)

• A semi-classical trace formula at a non-degenerate critical level

Cited by in corpus (4)

• Contributions of non-extremum critical points to the semi-classical trace formula
• Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential
• Spectral estimates for degenerate critical levels
• Asymptotic approximation of degenerate fiber integrals