Construction of Wavelet Sets Using Integral Self-Affine Multi-tiles |
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| Authors: | Xiaoye Fu Jean-Pierre Gabardo |
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| Institution: | 1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China
2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada
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| Abstract: | Gabardo and Yu first considered using integral self-affine tiles in the Fourier domain to construct wavelet sets and they produced a class of compact wavelet sets with certain self-similarity properties. In this paper, we generalize their results to the integral self-affine multi-tiles setting. We characterize some analytic properties of integral self-affine multi-tiles under certain conditions. We also consider the problem of constructing (multi)wavelet sets using integral self-affine multi-tiles. |
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