Abstract
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.
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7.6 Bibliographic notes
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(2007). Toeplitz Operators. In: Holomorphic Morse Inequalities and Bergman Kernels. Progress in Mathematics, vol 254. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8115-8_8
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DOI: https://doi.org/10.1007/978-3-7643-8115-8_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8096-0
Online ISBN: 978-3-7643-8115-8
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