Wavelet transform and orthogonal decomposition of L2 space on the cartan domain BDI(q = 2)

Abstract

Let G = (R+ × SO0(1,n)) × Rn+1 be the Weyl-Poincaré group and K AN be the Iwasawa decomposition of SOo(l, n) with K = SO(n). Then the "affine Weyl-Poincaré group" Ga = (R+. × AN) × Rn+1 can be realized as the complex tube domain II = 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 of the set of admissible wavelets associated to Ga is constructed, and it gives an orthogonal decomposition of L2 space on II (or the Cartan domain BDI(q = 2)) with every component Ak. being the range of wavelet transforms of functions in H2 with k. ©1997 American Mathematical Society.