Analytic Bergman operators in the semiclassical limit
Analysis of PDEs
2020-12-23 v2 Mathematical Physics
Complex Variables
Functional Analysis
math.MP
Abstract
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.
Cite
@article{arxiv.1808.00199,
title = {Analytic Bergman operators in the semiclassical limit},
author = {Ophélie Rouby and Johannes Sjoestrand and San Vu Ngoc},
journal= {arXiv preprint arXiv:1808.00199},
year = {2020}
}
Comments
70 pages. Revised version, to appear in Duke Math. Journal