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arXiv · 1311.2436

Equivariant spectral asymptotics for h-pseudodifferential operators

Tobias Weich
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Abstract

We prove equivariant spectral asymptotics for $ h$-pseudodifferential operators for compact orthogonal group actions generalizing results of El-Houakmi and Helffer (1991) and Cassanas (2006). Using recent results for certain oscillatory integrals with singular critical sets (Ramacher 2010) we can deduce a weak equivariant Weyl law. Furthermore, we can prove a complete asymptotic expansion for the Gutzwiller trace formula without any additional condition on the group action by a suitable generalization of the dynamical assumptions on the Hamilton flow.

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Tobias Weich. 2014-12-11. Equivariant spectral asymptotics for h-pseudodifferential operators. https://doi.org/10.1063/1.4896698

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