WAVELET TRANSFORM AND ORTHOGONAL DECOMPOSITION OF L-2 SPACE ON THE CARTAN DOMAIN BDI(Q=2)

Let G = (R(+) x SO0(1,n)) x Rn+1 be the Weyl-Poincare group and KAN b e the Iwasawa decomposition of SO0(1,n) with K = SO(n). Then the ''aff ine Weyl-Poincare' group'' G(a) = (R(+) x AN) x Rn+1 can be realized as the complex tube domain II = Rn+1 + iC or the classical Cartan doma in BDI(q = 2). The square-integrable representations of G and G(a) giv e the admissible wavelets and wavelet transforms. An orthogonal basis {psi(k)} of the set of admissible wavelets associated to G, is constru cted, and it gives an orthogonal decomposition of L-2 space on II (or the Cartan domain BDI(q = 2)) with every component A(k) being the rang e of wavelet transforms of functions in H-2 with psi(k).