Multivariate compactly supported C functions by subdivision

Maria Charina, Costanza Conti*, Nira Dyn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper discusses the generation of multivariate C functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called Up-function, by a non-stationary scheme based on masks of spline subdivision schemes of growing degrees, we term the multivariate functions we generate Up-like functions. We generate them by non-stationary schemes based on masks of three-directional box-splines of growing supports. To analyze the convergence and smoothness of these non-stationary schemes, we develop new tools which apply to a wider class of schemes than the class we study. With our method for achieving small compact supports, we obtain in the univariate case, Up-like functions with supports [0,1+ϵ] in comparison to the support [0,2] of the Up-function. Examples of univariate and bivariate Up-like functions are given. As in the univariate case, the construction of Up-like functions can motivate the generation of C compactly supported wavelets of small support in any dimension.

Original languageEnglish
Article number101630
JournalApplied and Computational Harmonic Analysis
Volume70
DOIs
StatePublished - May 2024

Keywords

  • Box-splines
  • Masks of increasing supports
  • Multivariate smoothing factors
  • Non-stationary subdivision schemes
  • Rvachev Up-function

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