Toeplitz Operators

Part of the Progress in Mathematics book series (PM, volume 254)


We show in this chapter how the asymptotic expansion of the Bergman kernel implies the semi-classical properties of Toeplitz operators acting on high tensor powers of a positive line bundle over a compact manifold. In particular we obtain a construction of a star-product (a deformation quantization) using this technique. Moreover, our approach works with some modifications on non-compact and symplectic manifolds.


Asymptotic Expansion Toeplitz Operator Formal Power Series Bergman Kernel Smooth Kernel 
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7.6 Bibliographic notes

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© Birkhäuser Verlag AG 2007

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