Supports of Locally Linearly Independent M-Refinable Functions,Attractors of Iterated Function Systems and Tilings |
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Authors: | Cheung Hoi Ling Tang Canqin Zhou Ding-Xuan |
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Institution: | (1) Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong;(2) Institute of Applied Mathematics, Hunan University, Changsha, Hunan, P. R. China, 410082 |
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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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Keywords: | refinable function support local linear independence attractor iterated function system self-affine tiling |
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