Spectral Asymptotics of Toeplitz Operators on Zoll Manifolds

We prove a generalization of the Strong Szegö Limit Theorem for Zoll type operators on smooth compact closed manifolds. More precisely, letXbe a compact manifold, and letQ:C∞(X)→C∞(X) be a self-adjoint first order ellipticΨDOwhose spectrum is {1, 2, 3, …}. LetAbe a zeroth orderΨDO onXwhose spectrum does not contain zero in its closed convex hull. WritePnfor the projector onto the span of the eigenfunctions ofQwith eigenvalues in {1, …, n}. Our main result is a second order asymptotic formula for log detPnAPn, asn→∞.