Search results for "70H15"

showing 2 items of 2 documents

Positivity, complex FIOs, and Toeplitz operators

2018

International audience; We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz operators on the Bargmann space is implied by the boundedness of their Weyl symbols.

Class (set theory)Pure mathematicsFourier integral operator in the complex domainPrimary: 32U05 32W25 35S30 47B35 70H1570H15Mathematics::Classical Analysis and ODEsOcean EngineeringCharacterization (mathematics)32U05 32W25 35S30 47B35 70H15Space (mathematics)01 natural sciencesMathematics - Analysis of PDEsQuadratic equation0103 physical sciencesFOS: Mathematics0101 mathematics[MATH]Mathematics [math]MathematicsMathematics::Functional Analysispositive canonical transformationMathematics::Complex Variables32U0532W25010102 general mathematicsToeplitz matrixFunctional Analysis (math.FA)Mathematics - Functional Analysis35S30Toeplitz operatorpositive Lagrangian plane010307 mathematical physicsstrictly plurisubharmonic quadratic form47B35Analysis of PDEs (math.AP)Toeplitz operator
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Analytic Bergman operators in the semiclassical limit

2018

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.

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 analysis
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