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A study of biorthogonal multiple vector-valued wavelets

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  • Han, Jincang
  • Cheng, Zhengxing
  • Chen, Qingjiang

Abstract

The notion of vector-valued multiresolution analysis is introduced and the concept of biorthogonal multiple vector-valued wavelets which are wavelets for vector fields, is introduced. It is proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. An algorithm for constructing a class of compactly supported biorthogonal multiple vector-valued wavelets is presented. Their properties are investigated by means of operator theory and algebra theory and time-frequency analysis method. Several biorthogonality formulas regarding these wavelet packets are obtained.

Suggested Citation

  • Han, Jincang & Cheng, Zhengxing & Chen, Qingjiang, 2009. "A study of biorthogonal multiple vector-valued wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1574-1587.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1574-1587
    DOI: 10.1016/j.chaos.2007.09.037
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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.
    3. Svozil, Karl, 2005. "Computational universes," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 845-859.
    4. El Naschie, M.S., 2006. "Hilbert space, the number of Higgs particles and the quantum two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 9-13.
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    1. Sun, Lei & Li, Gang, 2009. "Generalized orthogonal multiwavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2420-2424.

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