Equivariant local scaling asymptotics for smoothed Töplitz spectral projectors

Let X be the unit circle bundle of a positive line bundle on a Hodge manifold. We study the local scaling asymptotics of the smoothed spectral projectors associated with a first order elliptic Töplitz operator T on X, possibly in the presence of Hamiltonian symmetries. The resulting expansion is then used to give a local derivation of an equivariant Weyl law. It is not required that T be invariant under the structure circle action, that is, T needn't be a Berezin–Töplitz operator.