Constructive Approximation

, Volume 9, Issue 2–3, pp 123–166 | Cite as

On the construction of multivariate (pre)wavelets

  • Carl de Boor
  • Ronald A. DeVore
  • Amos Ron


A new approach for the construction of wavelets and prewavelets onRd from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL2(Rd) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution.

AMS classification

Primary 41A63 46C99 Secondary 41A30 41A15 42B99 46E20 

Key words and phrases

Wavelets Multiresolution Shift-invariant spaces Box splines 


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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Carl de Boor
    • 1
  • Ronald A. DeVore
    • 2
  • Amos Ron
    • 3
  1. 1.Center for Mathematical SciencesUniversity of Wisconsin-MadisonMadisonU.S.A.
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaU.S.A.
  3. 3.Computer Sciences DepartmentUniversity of Wisconsin-MadisonMadisonU.S.A.

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