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Regularity of refinable function vectors

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Abstract

We study the existence and regularity of compactly supported solutions φ = (φv) /r−1v=0 of vector refinement equations. The space spanned by the translates of φv can only provide approximation order if the refinement maskP has certain particular factorization properties. We show, how the factorization ofP can lead to decay of |̸v(u)| as |u| → ∞. The results on decay are used to prove uniqueness of solutions and convergence of the cascade algorithm.

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Authors and Affiliations

  1. Laboratoire d’Analyse Numerique, Université Pierre et Marie Curie, 4 Place Jussieu, 75005, Paris, Cedex 05, France

    Albert Cohen

  2. Department of Mathematics, Princeton University, 08544, Princeton, New Jersey

    Ingrid Daubechies

  3. Fachbereich Mathematik, Universität Rostock, D-18051, Rostock, Germany

    Gerlind Plonka

Authors
  1. Albert Cohen
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  2. Ingrid Daubechies
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  3. Gerlind Plonka
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Cohen, A., Daubechies, I. & Plonka, G. Regularity of refinable function vectors. The Journal of Fourier Analysis and Applications 3, 295–324 (1997). https://doi.org/10.1007/BF02649113

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