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A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor

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  • Sun, Lei
  • Zhang, Xiaozhong

Abstract

Biorthogonal wavelets can be constructed from the biorthogonal scaling functions. In this note, we consider a inverse proposition in high dimension wavelet with arbitrary matrix dilation factor and prove that if the wavelets are biorthogonal, then the associated scaling functions should be biorthogonal.

Suggested Citation

  • Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:2:p:711-715
    DOI: 10.1016/j.chaos.2008.03.002
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    References listed on IDEAS

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    1. El Naschie, M.S., 2006. "Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 39-42.
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    5. Sun, Lei & Cheng, Zhengxing & Huang, Yongdong, 2007. "Construction of trivariate biorthogonal compactly supported wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1412-1420.
    6. 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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