Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted -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 and for high powers of ample holomorphic line bundles over compact complex manifolds.
"Analytic Bergman operators in the semiclassical limit." Duke Math. J. 169 (16) 3033 - 3097, 1 November 2020. https://doi.org/10.1215/00127094-2020-0022