Analytic Bergman operators in the semiclassical limit

Ophélie Rouby (1) , Johannes Sjöstrand (2) , San Vu Ngoc (3)

1 Lycée Edouard Branly [Boulogne-sur-Mer]
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: adjoint operators; classical limit; kahler-metrics; kernel; quantization; asymptotics; theorem; space

Domaines: Mathématiques [math]

Ophélie Rouby, Johannes Sjöstrand, San Vu Ngoc. Analytic Bergman operators in the semiclassical limit. Duke Mathematical Journal, 2020, 169 (16), pp.3033-3097. ⟨10.1215/00127094-2020-0022⟩. ⟨hal-03036172⟩