论文信息 - A class of affine Wigner functions with extended covariance properties

A class of affine Wigner functions with extended covariance properties

Affine Wigner functions are phase space representations based on the affine group in place of the usual Weyl–Heisenberg group of quantum mechanics. Such representations are relevant to the time–frequency analysis of real signals. An interesting family is singled out by the requirement of covariance with respect to each solvable three‐parameter group containing the affine group. Explicit forms are given in each case and properties such as unitarity and localization are discussed. Some particular distributions are recovered.

P. Bertrand | J. Bertrand

[1] E. Wigner. On the quantum correction for thermodynamic equilibrium , 1932 .

[2] H. Margenau,et al. Correlation between Measurements in Quantum Theory , 1961 .

[3] L. Cohen. Generalized Phase-Space Distribution Functions , 1966 .

[4] N. Vilenkin. Special Functions and the Theory of Group Representations , 1968 .

[5] R. M. Dudley,et al. Lectures in Modern Analysis and Applications I , 1969 .

[6] Multipliers On Locally Compact Groups , 1969 .

[7] V. G. Romanov,et al. Integral Geometry and Inverse Problems for Hyperbolic Equations , 1974 .

[8] R. T. Sharp,et al. Invariants of real low dimension Lie algebras , 1976 .

[9] A. Kirillov. Elements of the theory of representations , 1976 .

[10] V. I. Tatarskii,et al. The Wigner representation of quantum mechanics , 1983 .

[11] M. Perroud. The fundamental invariants of inhomogeneous classical groups , 1983 .

[12] André Unterberger. The calculus of pseudo—differential operators of fuchs type , 1984 .

[13] La série discrète de ${\rm SL}(2,\,{R})$ et les opérateurs pseudo-différentiels sur une demi-droite , 1984 .

[14] Kurt Bernardo Wolf,et al. The metaplectic group within the Heisenberg-Weyl ring , 1986 .

[15] D. Wehner. High Resolution Radar , 1987 .

[16] L. Cohen,et al. Time-frequency distributions-a review , 1989, Proc. IEEE.