Constructive Approximation

, Volume 9, Issue 2, pp 123–166

On the construction of multivariate (pre)wavelets

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

DOI: 10.1007/BF01198001

Cite this article as:
de Boor, C., DeVore, R.A. & Ron, A. Constr. Approx (1993) 9: 123. doi:10.1007/BF01198001


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 41A6346C99Secondary 41A3041A1542B9946E20

Key words and phrases

WaveletsMultiresolutionShift-invariant spacesBox splines

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.