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Affine pseudoframes for subspaces of L2(R) associated with a generalized multiresolution structure

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  • Chen, Qingjiang
  • Cheng, Zhengxing
  • Wang, Cuiling

Abstract

In this paper, the notion of an m-band generalized multiresolution structure (GMS) of L2(R) is introduced. We give the definition and the characterization of affine pseudoframes for subspaces. The construction of a GMS of Paley–Wiener subspaces of L2(R) is investigated. The pyramid decomposition scheme is derived based on such a GMS. As a major new contribution the construction of affine frames for L2(R) based on a GMS is presented.

Suggested Citation

  • Chen, Qingjiang & Cheng, Zhengxing & Wang, Cuiling, 2007. "Affine pseudoframes for subspaces of L2(R) associated with a generalized multiresolution structure," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1401-1411.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1401-1411
    DOI: 10.1016/j.chaos.2006.05.032
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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.
    2. El Naschie, M.S., 2006. "Superstring theory: What it cannot do but E-infinity could," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 65-68.
    3. 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.
    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. Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and characterizations of orthogonal vector-valued multivariate wavelet packets," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1835-1844.

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