Wavelet transform on compact Gelfand pairs and its discretization

Using harmonic analysis on a compact Gelfand pair (G, K), we study the continuous wavelet analysis on the homogeneous space G/K. As example we give the wavelet associated with the K-biinvariant Poisson kernel on G. Next, using the previous results, we define and study three types of wavelet packets on G/K and the corresponding wavelet transforms. We prove for these transforms reconstruction formulas, and we describe the related multiresolution analysis.