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On asymptotic expansions of generalized Bergman kernels on symplectic manifolds
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A full off-diagonal asymptotic expansion is established for the generalized Bergman kernels of the renormalized Bochner Laplacians associated with high tensor powers of a positive line bundle over a compact symplectic manifold. As an application, the algebra of Toeplitz operators on the symplectic manifold associated with the renormalized Bochner Laplacian is constructed.
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Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold
On a closed symplectic manifold, the low-lying eigenvalues of the Bochner Laplacian on L^p are pτ0 + μj + O(p^{-1/2}), where μj are eigenvalues of model Toeplitz operators at the wells.
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