数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (S1): 58-67.
何建勋1, 彭立中2
He Jianxun1, Peng Lizhong2
摘要: Let Hn be the n-direct proded of Heisenbery group H, P the affine group of n. Then P ho a natural unitary representation U on L2(Hn). In this paper,the direct sum decomposition of irreducible invariant closed subspaces under unitary representation U for L2(Hn) is given. The restrictins of U on these subspaces are square-integrable. The charactedsation of admissible condition is obtained in ierms of the Fourier transform. By seleting appropriately an orthogonal wavelet basis and the wavelet transform,the authors obtain the orthogonal direct chin decomposinon of function space L2(P,dμ1).