Supports of locally linearly independent M-refinable functions, attractors of iterated function systems and tilings

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

2 Scopus Citations
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  • Hoi Ling Cheung
  • Canqin Tang
  • Ding-Xuan Zhou

Related Research Unit(s)


Original languageEnglish
Pages (from-to)257-268
Journal / PublicationAdvances in Computational Mathematics
Issue number3
Publication statusPublished - 2002


This paper is devoted to a study of supports of locally linearly independent M-relinable functions by means of attractors of iterated function systems, where M is an integer greater than (or equal to) 2. For this purpose, the local linear independence of shifts of M-relinable functions is required. So we give a complete characterization for this local linear independence property by finite matrix products, strictly in terms of the mask. We do this in a more general setting, the vector refinement equations. A connection between self-affine filings and L2 solutions of refinement equations without satisfying the basic sum rule is pointed out, which leads to many further problems. Several examples are provided to illustrate the general theory.

Research Area(s)

  • Attractor, Iterated function system, Local linear independence, Refinable function, Self-affine tiling, Support