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Wavelets with Frame Multiresolution Analysis

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A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V 0 admits a normalized tight frame (under translations). In this article, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer entries are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina at Charlotte, 28223, Charlotte, NC, USA, , , , ,

    X. Dai & Y. Diao

  2. Department of Mathematics, East China Normal University, Shanghai, China, , , , ,

    Q. Gu

  3. Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA, , , , ,

    D. Han

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  1. X. Dai
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  2. Y. Diao
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  3. Q. Gu
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  4. D. Han
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Dai, X., Diao, Y., Gu, Q. et al. Wavelets with Frame Multiresolution Analysis. J. Fourier Anal. Appl. 9, 39–48 (2003). https://doi.org/10.1007/s00041-003-0001-5

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  • DOI: https://doi.org/10.1007/s00041-003-0001-5

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