Self-Similar Lattice Tilings |
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Authors: | Karlheinz Grochenig Andrew Haas |
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Affiliation: | (1) Department of Mathematics U-9, University of Connecticut, Storrs, Connecticut 06269-3009, USA |
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Abstract: | We study the general question of the existence of self-similar lattice tilings of Euclidean space. A necessary and sufficient geometric condition on the growth of the boundary of approximate tiles is reduced to a problem in Fourier analysis that is shown to have an elegant simple solution in dimension one. In dimension two we further prove the existence of connected self-similar lattice tilings for parabolic and elliptic dilations. These results apply to produce Haar wavelet bases and certain canonical number systems. |
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