Weyl quantization and a symbol calculus for abelian groups

DOI10.1017/S1446788700008569zbMath1080.44002OpenAlexW2090114351MaRDI QIDQ5694828

Norman J. Wildberger

Publication date: 5 October 2005

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700008569

zbMATH Keywords

symplectic groupfinite groupsWeyl calculusHeisenberg groupLie algebracyclic groupssymbol calculusCayley transformMoyal productlinear transformationsCartan subalgebras

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Geometry and quantization, symplectic methods (81S10) Theta series; Weil representation; theta correspondences (11F27) Classical operational calculus (44A45)

Related Items (3)

Quantization of the affine group of a local field ⋮ Calculus of operators: covariant transform and relative convolutions ⋮ Gabor analysis over finite Abelian groups

Cites Work

• The Weil representation, Maslov index and theta series
• Quantum mechanics and partial differential equations
• Deformation theory and quantization. I: Deformations of symplectic structures
• Projective Fourier duality and Weyl quantization
• An algebra of pseudodifferential operators and quantum mechanics in phase space
• Sur certains groupes d'opérateurs unitaires
• Harmonic Analysis in Phase Space. (AM-122)
• The weyl calculus of pseudo-differential operators

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