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1 November 2020 Analytic Bergman operators in the semiclassical limit
Ophélie Rouby, Johannes Sjöstrand, San Vũ Ngọc
Duke Math. J. 169(16): 3033-3097 (1 November 2020). DOI: 10.1215/00127094-2020-0022

Abstract

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted L2-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 Cn and for high powers of ample holomorphic line bundles over compact complex manifolds.

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Ophélie Rouby. Johannes Sjöstrand. San Vũ Ngọc. "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

Information

Received: 6 August 2018; Revised: 4 March 2020; Published: 1 November 2020
First available in Project Euclid: 11 September 2020

MathSciNet: MR4167085
Digital Object Identifier: 10.1215/00127094-2020-0022

Subjects:
Primary: 32A25
Secondary: 32W25, 35A27, 47B35, 58J40, 70H15

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 16 • 1 November 2020
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