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Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix

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  • Chen, Qingjiang
  • Shi, Zhi

Abstract

In this paper, the notion of multiple vector-valued multiresolution analysis of space L2(Rs,Cr×r) is introduced. A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is investigated by means of time–frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of space L2(Rs,Cr×r) is obtained by constructing a series of subspaces of biorthogonal multiple vector-valued wavelet packets.

Suggested Citation

  • Chen, Qingjiang & Shi, Zhi, 2008. "Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 323-332.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:2:p:323-332
    DOI: 10.1016/j.chaos.2007.06.065
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    References listed on IDEAS

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    1. Chen, Qingjiang & Cheng, Zhengxing, 2007. "A study on compactly supported orthogonal vector-valued wavelets and wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 1024-1034.
    2. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
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    Cited by:

    1. 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.
    2. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and decomposition of biorthogonal vector-valued wavelets with compact support," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2765-2778.
    3. Chen, Qingjiang & Huo, Ailian, 2009. "The research of a class of biorthogonal compactly supported vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 951-961.
    4. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.

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