Nonlinear approximation theory on finite groups

Motivated by problems in signal recovery, we will investigate the distribution of the energy of the Fourier transform of a positive function on a finite group. In particular, we are able to bound from below the fraction of energy contained in various subsets of the Fourier transform of a positive function defined on a finite group. Applications to signal recovery for positive functions, as well as partial spectral analysis for data on finite groups are also presented.