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.
Berezin-Toeplitz quantization for eigenstates of the Bochner-Laplacian on symplectic manifolds
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abstract
We study the Berezin-Toeplitz quantization using as quantum space the space of eigenstates of the renormalized Bochner Laplacian corresponding to eigenvalues localized near the origin on a symplectic manifold. We show that this quantization has the correct semiclassical behavior and construct the corresponding star-product.
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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.