We develop a Fourier analysis for Radon transforms between multiplicity-free permutation representations. Statistical applications of such Radon transforms were given by Diaconis and Rockmore in [ Groups and Computation ( New Brunswick, NJ, 1991), DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 11, AMS, Providence, RI, 1993, pp. 87 - 104].
Fourier analysis of a class of finite radon transforms / Scarabotti, Fabio. - In: SIAM JOURNAL ON DISCRETE MATHEMATICS. - ISSN 0895-4801. - STAMPA. - 16:4(2003), pp. 545-554. [10.1137/s0895480102416398]