Weyl symbolic calculus on any Lie group

DOI10.1007/BF00992755zbMath0779.22005WikidataQ115394641 ScholiaQ115394641MaRDI QIDQ1802852

Dominique Manchon

Publication date: 29 June 1993

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

Weyl calculusLie algebraunitary representationsdiffeomorphismspseudodifferential operatorselliptic operatorsCampbell-Hausdorff formulaWeyl spectral asymptotic formula

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Analysis on real and complex Lie groups (22E30) Pseudodifferential and Fourier integral operators on manifolds (58J40) General properties and structure of real Lie groups (22E15)

Related Items (5)

Beyond the classical Weyl and Colin de Verdière's formulas for Schrödinger operators with polynomial magnetic and electric fields ⋮ Quantization of the affine group of a local field ⋮ Opérateurs pseudodifférentiels et représentations unitaires des groupes de Lie ⋮ Quantum evolution and sub-Laplacian operators on groups of Heisenberg type ⋮ Finite difference operators, pseudo-differential calculus and representations of Lie groups

Cites Work

• Parametrix constructions for right invariant differential operators on nilpotent groups
• Regular * representations of Lie algebras
• An explicit *-product on the cotangent bundle of a Lie group
• An associative algebra of functions on the orbits of nilpotent Lie groups
• Symbolic calculus on nilpotent Lie groups and applications
• The Campbell-Hausdorff formula and invariant hyperfunctions
• The Weyl functional calculus
• On the Weyl functional calculus
• Espaces symétriques et méthode de Kashiwara-Vergne
• Formule de Weyl pour les groupes de Lie nilpotents.
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