Equivariant spectral asymptotics for h-pseudodifferential operators

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.

Updated references and some minor changes and corrections of typos

References in corpus (3)

• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
• Singular equivariant asymptotics and Weyl's law
• Reduced Gutzwiller formula with symmetry: case of a finite group