  Spin-tomographic symbols of qudit states and spin observables are studied.
Spin observables are associated with the functions on a manifold whose points
are labelled by spin projections and 2-sphere coordinates. The star-product
kernel for such functions is obtained in explicit form and connected with
Fourier transform of characters of SU(2) irreducible representation. The
kernels are shown to be in close relation to the Chebyshev polynomials. Using
specific properties of these polynomials, we establish the recurrence relation
between kernels for different spins. Employing the explicit form of the
star-product kernel, a sum rule for Clebsch-Gordan and Racah coefficients is
derived. Explicit formulas are obtained for the dual tomographic star-product
kernel as well as for intertwining kernels which relate spin-tomographic
symbols and dual tomographic symbols.
