Equivariant spectral asymptotics for hpseudodifferential operators
Abstract
We prove equivariant spectral asymptotics for hpseudodifferential operators for compact orthogonal group actions generalizing results of El Houakmi and Helffer ["Comportement semiclassique en présence de symétries: Action d'un groupe de Lie compact," Asymp. Anal. 5(2), 91113 (1991)] and Cassanas ["Reduced Gutzwiller formula with symmetry: Case of a Lie group," J. Math. Pures Appl. 85(6), 719742 (2006)]. Using recent results for certain oscillatory integrals with singular critical sets [P. Ramacher, "Singular equivariant asymptotics and Weyl's law: On the distribution of eigenvalues of an invariant elliptic operator," J. Reine Angew. Math. (Crelles J.) (to be published)], 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.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 October 2014
 DOI:
 10.1063/1.4896698
 arXiv:
 arXiv:1311.2436
 Bibcode:
 2014JMP....55j1501W
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Spectral Theory
 EPrint:
 Updated references and some minor changes and corrections of typos