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A direct approach to the analytic Bergman projection
Alix Deleporte1; Michael Hitrik2; Johannes Sjöstrand3
1 Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Department of Mathematics, University of California, Los Angeles CA 90095-1555, USA
3 IMB (UMR 5584 CNRS), Université de Bourgogne 9, Av. A. Savary, BP 47870 FR-21078 Dijon, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 1, pp. 153-176.

We develop a direct approach to the semiclassical asymptotics for Bergman projections in exponentially weighted spaces of holomorphic functions, with real analytic strictly plurisubharmonic weights. In particular, the approach does not make any direct use of the Kuranishi trick and it allows us to shorten and simplify proofs of a result due to [7] and [23], stating that in the analytic case, the amplitude of the asymptotic Bergman projection is a realization of a classical analytic symbol.

Nous développons une approche directe pour l’asymptotique semiclassique du projecteur de Bergman sur des espaces de fonctions holomorphes à poids exponentiel, dont le poids est analytique et strictement pluri-sous-harmonique. En particulier, cette approche n’utilise jamais directement l’astuce de Kuranishi et nous permet de raccourcir et de simplifier les preuves du fait, établi dans [7] et [23], que dans le cas analytique, l’amplitude du projecteur de Bergman asymptotique est la réalisation d’un symbole analytique classique.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1765

Alix Deleporte 1; Michael Hitrik 2; Johannes Sjöstrand 3

1 Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Department of Mathematics, University of California, Los Angeles CA 90095-1555, USA
3 IMB (UMR 5584 CNRS), Université de Bourgogne 9, Av. A. Savary, BP 47870 FR-21078 Dijon, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Alix Deleporte; Michael Hitrik; Johannes Sjöstrand. A direct approach to the analytic Bergman projection. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 33 (2024) no. 1, pp. 153-176. doi : 10.5802/afst.1765. https://afst.centre-mersenne.org/articles/10.5802/afst.1765/

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