On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields

We consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere which was recently introduced in the literature. We provide necessary and sufficient conditions for these coefficients to be asymptotic uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high resolution sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data.