Cubic spline prewavelets on the four-directional mesh

M. D. Buhmann, O. Davydov, T .N. T. Goodman

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
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In this paper, we design differentiable, two dimensional, piecewise polynomial cubic prewavelets of particularly small compact support. They are given in closed form, and provide stable, orthogonal decompositions of $L^2(\RR^2)$. In particular, the splines we use in our prewavelet constructions give rise to stable bases of spline spaces that contain all cubic polynomials, whereas the more familiar box spline constructions cannot reproduce all cubic polynomials, unless resorting to a box spline of higher polynomial degree.
Original languageEnglish
Pages (from-to)113-133
Number of pages21
JournalFoundations of Computational Mathematics
Issue number2
Early online date17 Jan 2003
Publication statusPublished - 31 May 2003


  • prewavelets
  • cubic polynomials
  • spline constructions


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