ANALYTIC BERGMAN OPERATORS IN THE SEMICLASSICAL LIMIT

被引：11

作者：

Rouby, Ophelie ^{[1
]}

Sjostrand, Johannes ^{[2
]}

San Vu Ngoc ^{[3
]}

机构：

[1] Lycee Edouard Branly, Boulogne Sur Mer, France

[2] Univ Bourgogne, CNRS, Dijon, France

[3] Univ Rennes, CNRS, Rennes, France

来源：

DUKE MATHEMATICAL JOURNAL | 2020年 / 169卷 / 16期

关键词：

ADJOINT OPERATORS; CLASSICAL LIMIT; KAHLER-METRICS; KERNEL; QUANTIZATION; ASYMPTOTICS; THEOREM; SPACE;

D O I：

10.1215/00127094-2020-0022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 C-n and for high powers of ample holomorphic line bundles over compact complex manifolds.

引用

页码：3033 / 3097

页数：65

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