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We present a detailed discussion of a general theory of phase-spacedistributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9(1998)]. This theory provides a unified phase-space formulation of quantummechanics for physical systems possessing Lie-group symmetries. The concept ofgeneralized coherent states and the method of harmonic analysis are used toconstruct explicitly a family of phase-space functions which are postulated tosatisfy the Stratonovich-Weyl correspondence with a generalized tracialitycondition. The symbol calculus for the phase-space functions is given by meansof the generalized twisted product. The phase-space formalism is used to studythe problem of the reconstruction of quantum states. In particular, we considerthe reconstruction method based on measurements of displaced projectors, whichcomprises a number of recently proposed quantum-optical schemes and is alsorelated to the standard methods of signal processing. A general group-theoreticdescription of this method is developed using the technique of harmonicexpansions on the phase space.Comment: REVTeX, 18 pages, no figure

Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries