Quantum tomography with wavelet transform in Banach space on homogeneous space

In this study the intimate connection is established between the Banach space wavelet reconstruction method on homogeneous spaces with both singular and nonsingular vacuum vectors, and some of the well known quantum tomographies, such as: Moyal-representation for a spin, discrete phase space tomography, tomography of a free particle, Homodyne tomography, phase space tomography and SU(1,1) tomography. And both the atomic decomposition and the Banach frame nature of these quantum tomographic examples are also revealed in details. Finally the connection between the wavelet formalism on Banach space and Q-function is discussed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007