Wavelet Transform and Orthogonal Decomposition of L2 Space on the Cartan Domain BDI(q=2)

Let G = R + SO0(1;n ) nR n+1 be the Weyl-Poincare group and KAN be the Iwasawa decomposition of SO0(1;n )w ith K =SO(n). Then the \ane Weyl-Poincare group" Ga = R + AN nR n+1 can be realized as the complex tube domain = Rn+1 +iC or the classical Cartan domain BDI(q = 2). The square-integrable representations of G and Ga give the admissible wavelets and wavelet transforms. An orthogonal basis f kg of the set of admissible wavelets associated to Ga is constructed, and it gives an orthogonal decomposition of L2 space on (or the Cartan domain BDI(q = 2)) with every component Ak being the range of wavelet transforms of functions in H2 with k.