6533b837fe1ef96bd12a29bc
RESEARCH PRODUCT
Analytic Bergman operators in the semiclassical limit
San Vũ NgọcOphélie RoubyJohannes Sjöstrandsubject
Pure mathematicsadjoint operatorsMicrolocal analysis32A2501 natural sciences[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Limit (mathematics)Bergman projectionComplex Variables (math.CV)[MATH]Mathematics [math]Mathematics::Symplectic GeometryMathematical PhysicsBergman kernelMathematicsasymptotic expansionweighted L2-estimates58J40[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]Mathematical Physics (math-ph)16. Peace & justiceFunctional Analysis (math.FA)Mathematics - Functional Analysisasymptoticstheoremkernelanalytic pseudodifferential operator010307 mathematical physicsAsymptotic expansion47B35classical limitAnalysis of PDEs (math.AP)Toeplitz operatorGeneral Mathematics70H15Holomorphic functionFOS: Physical sciencesSemiclassical physicsKähler manifold[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]analytic symbolsMathematics - Analysis of PDEskahler-metrics0103 physical sciencesFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsMathematics - Complex VariablesMathematics::Complex Variables010102 general mathematics32W25space35A27Kähler manifoldmicrolocal analysisToeplitz operatorquantizationsemiclassical analysisdescription
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 $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-07-30 |