Quantization of compact symplectic manifolds
arXiv:1409.8507
Abstract
We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.
Simplified the main proofs on operator composition and added sharp remainder estimates. Version 1 has been published in Journal of Geometric Analysis