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Advances in Computational Mathematics

, Volume 18, Issue 2–4, pp 269–296 | Cite as

Quasi-Biorthogonal Frame Multiresolution Analyses and Wavelets

  • Hong Oh Kim
  • Rae Young Kim
  • Jae Kun Lim
Article

Abstract

We introduce the concepts of quasi-biorthogonal frame multiresolution analyses and quasi-biorthogonal frame wavelets which are natural generalizations of biorthogonal multiresolution analyses and biorthogonal wavelets, respectively. Necessary and sufficient conditions for quasi-biorthogonal frame multiresolution analyses to admit quasi-biorthogonal wavelet frames are given, and a non-trivial example of quasi-biorthogonal frame multiresolution analyses admitting quasi-biorthogonal frame wavelets is constructed. Finally, we characterize the pair of quasi-biorthogonal frame wavelets that is associated with quasi-biorthogonal frame multiresolution analyses.

wavelets frames multiresolution analysis shift-invariant spaces 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Hong Oh Kim
    • 1
  • Rae Young Kim
    • 1
  • Jae Kun Lim
    • 2
  1. 1.Division of Applied MathematicsKAISTTaejonKorea
  2. 2.CHiPSKAISTTaejonKorea

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