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.
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.
Accepté le :
Publié le :
Alix Deleporte 1 ; Michael Hitrik 2 ; Johannes Sjöstrand 3
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@article{AFST_2024_6_33_1_153_0, author = {Alix Deleporte and Michael Hitrik and Johannes Sj\"ostrand}, title = {A direct approach to the analytic {Bergman} projection}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {153--176}, publisher = {Universit\'e Paul Sabatier, Toulouse}, volume = {Ser. 6, 33}, number = {1}, year = {2024}, doi = {10.5802/afst.1765}, language = {en}, url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1765/} }
TY - JOUR AU - Alix Deleporte AU - Michael Hitrik AU - Johannes Sjöstrand TI - A direct approach to the analytic Bergman projection JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2024 SP - 153 EP - 176 VL - 33 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1765/ DO - 10.5802/afst.1765 LA - en ID - AFST_2024_6_33_1_153_0 ER -
%0 Journal Article %A Alix Deleporte %A Michael Hitrik %A Johannes Sjöstrand %T A direct approach to the analytic Bergman projection %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2024 %P 153-176 %V 33 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1765/ %R 10.5802/afst.1765 %G en %F AFST_2024_6_33_1_153_0
Alix Deleporte; Michael Hitrik; Johannes Sjöstrand. A direct approach to the analytic Bergman projection. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 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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