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arXiv · 1808.00199

Analytic Bergman operators in the semiclassical limit

Ophélie Rouby·Johannes Sjoestrand·San Vu Ngoc
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Abstract

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ 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 $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.

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BibTeXRIS

Ophélie Rouby, Johannes Sjoestrand, San Vu Ngoc. 2018-08-01. Analytic Bergman operators in the semiclassical limit. https://doi.org/10.1215/00127094-2020-0022

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