Abstract
This paper is devoted to a study of supports of locally linearly independent M-refinable 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-refinable 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 tilings and L 2 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.
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Cheung, H.L., Tang, C. & Zhou, DX. Supports of Locally Linearly Independent M-Refinable Functions, Attractors of Iterated Function Systems and Tilings. Advances in Computational Mathematics 17, 257–268 (2002). https://doi.org/10.1023/A:1011906532250
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DOI: https://doi.org/10.1023/A:1011906532250