Analytic Bergman operators in the semiclassical limit

@article{Rouby2018AnalyticBO,
  title={Analytic Bergman operators in the semiclassical limit},
  author={O. Rouby and J. Sjoestrand and S. V. Ngoc},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
Using a new quantization scheme, we construct approximate semi-classical Bergman projections on weighted L² spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on C^n and for high powers of ample holomorphic line bundles over compact complex manifolds. 
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