Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on ...Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.展开更多
文摘Let P be the transform group on R n, then P has a natural unitary representation U on L 2(R n). Decompose L 2(R n) into the direct sum of irreducible invariant closed subspaces. The restriction of U on these subspaces is square integrable. In this paper the characterization of admissible condition in terms of the Fourier transform is given. The wavelet transform is defined, and the orthogonal direct sum decomposition of function space L 2(P,dμ l) ) is obtained.
