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A note on the standard dual frame of a wavelet frame with three-scale

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Listed:
  • Chen, Qingjiang
  • Wei, Zongtian
  • Feng, Jinshun

Abstract

In this paper, it is shown that there exist wavelet frames generated by two functions which have good dual wavelet frames, but for which the standard dual wavelet frame does not consist of wavelets. That is to say, the standard dual wavelet frame cannot be generated by the translations and dilations of a single function. Relation to some physical theories such as entropy and E-infinity theory is also discussed.

Suggested Citation

  • Chen, Qingjiang & Wei, Zongtian & Feng, Jinshun, 2009. "A note on the standard dual frame of a wavelet frame with three-scale," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 931-937.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:931-937
    DOI: 10.1016/j.chaos.2009.02.024
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    References listed on IDEAS

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    1. 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.
    2. Agop, M. & Stroe, A. & Murgulet, C., 2006. "El Naschie’s space–time and gravitational instanton in Weyl–Dirac theory," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 306-312.
    3. El Naschie, M.S., 2006. "Superstrings, entropy and the elementary particles content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 48-54.
    4. El Naschie, M.S., 2008. "String theory, exceptional Lie groups hierarchy and the structural constant of the universe," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 7-12.
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