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Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale

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  • Chen, Qingjiang
  • Cao, Huaixin
  • Shi, Zhi

Abstract

The notion of vector-valued multiresolution analysis of space L2(R,Cs×s) is introduced and the definition of orthogonal multiple vector-valued wavelets with 4-scale is given. First we obtain a necessary and sufficient condition on the existence of orthogonal multiple vector-valued wavelets by means of paraunitary vector filter bank theory. Second we propose an algorithm for constructing a class of compactly supported orthogonal multiple vector-valued wavelets. Finally, the notion of orthogonal multiple vector-valued wavelet packets is introduced. Their characterizations are presented by virtue of matrix theory, time–frequency analysis method and operator theory. In particular, orthonormal bases of space L2(R,Cs×s) are constructed from these wavelet packets. Relation to some physical theories such as E-infinity theory is also discussed.

Suggested Citation

  • Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Design and characterizations of a class of orthogonal multiple vector-valued wavelets with 4-scale," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 91-102.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:91-102
    DOI: 10.1016/j.chaos.2007.11.014
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    References listed on IDEAS

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    1. Agop, M. & Vasilica, M., 2006. "El Naschie’s supergravity by means of the gravitational instantons synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 318-323.
    2. 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.
    3. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    4. He, Ji-Huan, 2007. "E-Infinity theory and the Higgs field," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 782-786.
    5. 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.
    6. 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.
    7. Svozil, Karl, 2005. "Computational universes," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 845-859.
    8. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    9. 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.
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