Constructive Approximation

, Volume 17, Issue 4, pp 479–514 | Cite as

Commutation for Irregular Subdivision

  • Ingrid Daubechies
  • Igor Guskov
  • Wim Sweldens
Article

Abstract.

We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.

Key words. Irregular samples, Subdivision, Scaling function, Wavelet, Commutation, Spline, Finite difference. AMS Classification. 41A15, 42C40, 65D07, 47B39. 

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Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • Ingrid Daubechies
    • 1
  • Igor Guskov
    • 2
  • Wim Sweldens
    • 3
  1. 1.Program for Applied and Computational Mathematics Princeton University Princeton, NJ 08544 USA ingrid@math.princeton.eduUS
  2. 2.Program for Applied and Computational Mathematics Princeton University Princeton, NJ 08544 USA ivguskov@math.princeton.eduUS
  3. 3.Lucent Technologies Bell Laboratories Room 2C-376 600 Mountain Avenue Murray Hill, NJ 07974 USA wim@bell-labs.comUS

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