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Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function

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  • Yuan, De-you
  • Du, Shu-de
  • Cheng, Zheng-xing

Abstract

The notion of vector-valued wavelets associated with an orthogonal vector-valued scaling function with 3-scale is introduced. The existence of orthogonal vector-valued wavelets is discussed and a necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a class of orthogonal vector-valued wavelets with compact support is proposed. The concept of vector-valued wavelet packets is introduced and their properties are characterized by virtue of operator theory, time–frequency analysis method. Moreover, it is shown how to construct various orthonormal bases of space L2(R,Cμ)(2⩽μ∈Z) from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.

Suggested Citation

  • Yuan, De-you & Du, Shu-de & Cheng, Zheng-xing, 2009. "Design and properties of vector-valued wavelets associated with an orthogonal vector-valued scaling function," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1368-1376.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1368-1376
    DOI: 10.1016/j.chaos.2008.05.016
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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. Iovane, G. & Gargiulo, G. & Zappale, E., 2006. "A Cantorian potential theory for describing dynamical systems on El Naschie’s space–time," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 588-598.
    4. El Naschie, M.S., 2007. "Feigenbaum scenario for turbulence and Cantorian E-infinity theory of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 911-915.
    5. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    6. Giordano, P. & Iovane, G. & Laserra, E., 2007. "El Naschie ϵ(∞) Cantorian structures with spatial pseudo-spherical symmetry: A possible description of the actual segregated universe," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1108-1117.
    7. 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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