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Quasi-Biorthogonal Frame Multiresolution Analyses and Wavelets

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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.

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Authors and Affiliations

  1. Division of Applied Mathematics, KAIST, 373-1 Kusong-Dong Yusong-Gu, Taejon, 305-701, Korea

    Hong Oh Kim & Rae Young Kim

  2. CHiPS, KAIST, 373-1 Kusong-Dong Yusong-Gu, Taejon, 305-701, Korea

    Jae Kun Lim

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  1. Hong Oh Kim
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  2. Rae Young Kim
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Kim, H.O., Kim, R.Y. & Lim, J.K. Quasi-Biorthogonal Frame Multiresolution Analyses and Wavelets. Advances in Computational Mathematics 18, 269–296 (2003). https://doi.org/10.1023/A:1021371227388

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