Abstract
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→∞.
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