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The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix

Author

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  • Wang, Xiao-Feng
  • Gao, Hongwei
  • Jinshun, Feng

Abstract

In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an arbitrary integer-valued dilation matrix. A novel method for constructing higher-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packets. Finally, several orthonormal wavelet packet bases of L2(Rs)r are constructed from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Suggested Citation

  • Wang, Xiao-Feng & Gao, Hongwei & Jinshun, Feng, 2009. "The characterization of vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1959-1966.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:1959-1966
    DOI: 10.1016/j.chaos.2009.03.200
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    References listed on IDEAS

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