Kernel of star-product for spin tomograms

The spin-state tomogram is presented as the modulus squared of the matrix element of the SU(2)-group irreducible representation. For the spin system, we established explicitly a realization of the set of operators defining for spin tomograms the star-product formalism in terms of irreducible tensors. On the set of spin tomograms, the delta-function and 'standard' and Moyal-like kernels of the tomograrn star-product are calculated explicitly in terms of Clebsch-Gordan and Racah coefficients and matrix elements of the SU(2) irreducible representation. In the limit of infinite spin, the spin tomogram is shown to become the tomogram of the harmonic-oscillator state.