THE SPECTRAL DENSITY FUNCTION OF THE RENORMALIZED BOCHNER LAPLACIAN ON A SYMPLECTIC MANIFOLD

摘要

We consider the renormalized Bochner Laplacian acting on tensor powers of a positive line bundle on a compact symplectic manifold. We derive an explicit local formula for the spectral density function in terms of coefficients of the Riemannian metric and symplectic form.