We study semiclassical sequences of distributions uh associated with a Lagrangian submanifold of phase space L⊂ T∗X. If uh is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on L, then the asymptotics of uh are well understood by work of Arnol’d, provided L projects to X with a stable simple Lagrangian singularity. We establish sup-norm estimates on uh under much more general hypotheses on the rate at which it is concentrating on L (again assuming a stable simple projection). These estimates apply to sequences of eigenfunctions of integrable and KAM Hamiltonians.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics