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Admissible wavelets associated with the transform group on Rn

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Abstract

Let P be the transform group on R n, then P has a natural unitary representation U on L2(R n). Decompose L2(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 1 )) is obtained.

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Authors and Affiliations

  1. Mathematics Department, Nanjing Normal University, 210097, Nanjing

    He Jianxun & Peng Lizhong

  2. Mathematics Department, Peking University, 100871, Beijing

    He Jianxun & Peng Lizhong

Authors
  1. He Jianxun
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  2. Peng Lizhong
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Additional information

This works is supported by the National Natural Science Foundation of China and the Science Foundation of Shandong Education Commission.

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Jianxun, H., Lizhong, P. Admissible wavelets associated with the transform group on Rn . Appl. Math. Chin. Univ. 12, 473–482 (1997). https://doi.org/10.1007/s11766-997-0050-7

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  • DOI: https://doi.org/10.1007/s11766-997-0050-7

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