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 GrK. 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 GrK and the corresponding wavelet transforms. We prove for these transforms reconstruction formulas, and we describe the related multiresolution analysis.