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Admissible wavelets associated with the classical domain of type one

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Approximation Theory and its Applications

Abstract

The classical domain of type one has an unbounded realization as the Siegel domainD(Φ, Ω) by the Cayley transform. LetP be the Iwasawa subgroup of the affine automorphisms group ofD(Φ, Ω), thenP has a natural unitary representation U on\(L^2 (\Re )\). We decompose\(L^2 (\Re )\) into the direct sum of the irreducible invariant closed subspaces under U, and give the characterization of the admissible condition in terms of the Fourier transform. Define the wavelet transform, we obtain the direct sum decomposition of L2(D(Φ, Ω), dμ).

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, 210097, Nanjing, P.R. China

    He Jianxun

  2. Department of Mathematics, Peking University, 100871, Beijing, P.R. China

    Liu Heping

Authors
  1. He Jianxun
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  2. Liu Heping
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Correspondence to He Jianxun.

Additional information

The work for this paper was supported by the National Natural Science Foundation of China and the Foundation of Educational Commission of Shangdong Provience.

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Jianxun, H., Heping, L. Admissible wavelets associated with the classical domain of type one. Approx. Theory & its Appl. 14, 89–105 (1998). https://doi.org/10.1007/BF02836770

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  • DOI: https://doi.org/10.1007/BF02836770

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