The spectral density function of the renormalized Bochner Laplacian on a symplectic manifold

Abstract

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.

v2: several typos corrected, v3: final version

References in corpus (4)

• Toeplitz operators on symplectic manifolds
• Trace formula for the magnetic Laplacian
• Donaldson's $Q$-operators for symplectic manifolds
• Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold