A pseudo-differential calculus on non-standard symplectic space; spectral and regularity results in modulation spaces

DOI10.1016/j.matpur.2011.07.006zbMath1232.53069arXiv1209.1849OpenAlexW2964194272WikidataQ39588452 ScholiaQ39588452MaRDI QIDQ650843

Franz Luef, João Nuno Prata, Nuno Costa Dias, Maurice A. De Gosson

Publication date: 7 December 2011

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.1849

zbMATH Keywords

Weyl calculusmodulation spacespseudo-differential operatorsFeichtinger's spacesSHubin's symbolspectral and regularity resuts

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55)

Related Items

Quantum dynamics in phase space: Moyal trajectories 3 ⋮ An Excursion to Multiplications and Convolutions on Modulation Spaces ⋮ Born-Jordan pseudodifferential calculus, Bopp operators and deformation quantization ⋮ Gabor products and a phase space approach to nonlinear analysis ⋮ Quantum mechanics in phase space: the Schrödinger and the Moyal representations ⋮ A symplectic extension map and a new Shubin class of pseudo-differential operators ⋮ Quantum dynamics in phase space: Moyal trajectories 2 ⋮ Gaussian distributions and phase space Weyl-Heisenberg frames ⋮ Deformation of noncommutative quantum mechanics ⋮ Wigner functions on non-standard symplectic vector spaces ⋮ METAPLECTIC FORMULATION OF THE WIGNER TRANSFORM AND APPLICATIONS ⋮ Wigner analysis of operators. I: Pseudodifferential operators and wave fronts

Cites Work

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• Spectral and regularity properties of a pseudo-differential calculus related to Landau quantization
• Wigner measures in noncommutative quantum mechanics
• Time-frequency analysis of Sjöstrand's class
• Quantum states and Hardy's formulation of the uncertainty principle: a symplectic approach
• A new approach to the \(*\)-genvalue equation
• The symplectic camel and the uncertainty principle: the tip of an iceberg?
• On a new Segal algebra
• Deformation theory and quantization. I: Deformations of symplectic structures
• Deformation theory and quantization. II: Physical applications
• Weyl transforms
• Remarks on a Wiener type pseudodifferential algebra and Fourier integral operators
• Hermite functions and uncertainty principles for the Fourier and the windowed Fourier trans\-forms.
• Foundations of time-frequency analysis
• On the twisted convolution product and the Weyl transformation of tempered distributions
• Continuity properties for modulation spaces, with applications to pseudo-differential calculus. II
• An algebra of pseudodifferential operators
• The uncertainty principle and positivity of trace-class operators: applications to density operators
• Composition and spectral invariance of pseudodifferential operators on modulation spaces
• Symplectic geometry and quantum mechanics
• Hardy's Theorem and the Short-Time Fourier Transform of Schwartz Functions
• Integral bounds for radar ambiguity functions and Wigner distributions
• Spectral Properties of a Class of Generalized Landau Operators
• On the usefulness of modulation spaces in deformation quantization
• Phase-space noncommutative quantum cosmology
• The weyl calculus of pseudo-differential operators
• A deformation quantization theory for noncommutative quantum mechanics
• Weyl–Wigner formulation of noncommutative quantum mechanics
• Noncommutative field theory
• Quantum field theory on noncommutative spaces

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