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Sur la formule semi-classique des traces. (On the semi-classical trace formula). (French. Abridged English version) Zbl 0738.58046
For a class of \(h\)-pseudo-differential operators \(a(x,hD_ x)\) on the manifold \(M\) the asymptotics of \[ L(m,\varphi)=(1/m)\sum_{1\leq k\leq m}\hbox{Tr }\varphi[(a(x,hD_ x)-E)/h]\mid_{h=1/k} \] is obtained for \(m\to+\infty\) where \(\varphi\) is the function with the Fourier transform \(\hat\varphi\in C^ \infty_ 0\) vanishing of the order \(\dim M\) at 0. The limit of \(L(m,\varphi)\) is calculated in terms of the periodic Hamiltonian trajectories of the principal symbol.

MSC:
58J40 Pseudodifferential and Fourier integral operators on manifolds
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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