Wigner Functions for a Class of Semidirect Product Groups

Abstract

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations from the discrete series and each unitary irreducible representation is associated with a coadjoint orbit. The set of all coadjoint orbits (hence UIRs) is finite and their union is dense in the dual of the Lie algebra. The simple structure of the groups and the orbits enables us to compute the various quantities appearing in the definition of the Wigner function explicitly. Possible use of the Wigner functions so constructed, in image analysis and quantum optical measurements, is suggested.

40 pages

References in corpus (1)

• Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions

Cited by in corpus (6)

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• A survey on Weyl calculus for representations of nilpotent Lie groups
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• Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type
• Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions
• Heisenberg groups and their automorphisms over algebras with central involution