0000000000319667

AUTHOR

L. A. Coburn

showing 2 related works from this author

Weyl symbols and boundedness of Toeplitz operators

2019

International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

Mathematics::Functional AnalysisMathematics - Complex VariablesMathematics::Operator AlgebrasGeneral Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEs32U05 32W25 35S30 47B3501 natural sciencesToeplitz matrixFunctional Analysis (math.FA)AlgebraMathematics - Functional AnalysisFOS: MathematicsComputer Science::Symbolic Computation0101 mathematicsComplex Variables (math.CV)[MATH]Mathematics [math]Mathematics
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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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