Acta mathematica scientia,Series B ›› 1998, Vol. 18 ›› Issue (S1): 58-67.
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He Jianxun1, Peng Lizhong2
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Abstract: 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).
Key words: Admissible condition, Wavelet transform, Heisenbery group, Orthogonal direct sum decomposition, Generalized upper half-plance
He Jianxun, Peng Lizhong. ADMISSIBLE WAVELETS ON THE PRODUCT HEISENBERG GROUP Hn[J].Acta mathematica scientia,Series B, 1998, 18(S1): 58-67.
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