Microlocal Weyl formula on contact manifolds

Abstract

If M is a compact, contact manifold, with contact line bundle Σ, L a “sublaplacian” on M, characteristic on and if is an orthonormal basis of eigenfunctions of –L, with eigenvalues then concentrates microlocally on We study a microlocal Weyl formula, giving the limit as of for a class of pseudodifferential operators A on M. Such a limit for the algebra of classical pseudodifferential operators, was evaluated by Colin, Hillairet, and Trelat and used to study quantum ergodic theorems on compact 3 D contact manifolds. Here we take A to belong to a different pseudodifferential operator algebra, tuned to the contact structure of M. This produces a Weyl formula exhibiting richer behavior than one sees for