Search results for " 47B35"

showing 4 items of 4 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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Characterizing boundedness of metaplectic Toeplitz operators

2023

We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger-Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.

Mathematics - Functional Analysis32A36 32U05 32W25 35S30 47B35Mathematics - Complex VariablesFOS: MathematicsComplex Variables (math.CV)Functional Analysis (math.FA)
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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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On a generalisation of Krein's example

2017

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.

Pure mathematicsClassical exampleApplied Mathematics010102 general mathematicsFOS: Physical sciencesMultiplicity (mathematics)Mathematical Physics (math-ph)01 natural sciencesUnitary stateFunctional Analysis (math.FA)Primary 47B15 Secondary 47A55 35J25 47A10 47B35Mathematics - Functional AnalysisMathematics - Spectral Theory0103 physical sciencesFOS: MathematicsComputer Science::Symbolic Computation010307 mathematical physics0101 mathematicsSpectral Theory (math.SP)Mathematical PhysicsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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