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Three-way tiling sets in two dimensions.
Acta Appl. Math. 108, 529-546 (2009)
In this article we show that there exist measurable sets W subset of R-2 with finite measure that tile R-2 in a measurable way under the action of a expansive matrix A, an affine Weyl group (W) over tilde, and a full rank lattice (Gamma) over tilde subset of R-2. This note is follow- up research to the earlier article "Coxeter groups and wavelet sets" by the first and second authors, and is also relevant to the earlier article "Coxeter groups, wavelets, multiresolution and sampling" by M. Dobrescu and the third author. After writing these two articles, the three authors participated in a workshop at the Banff Center on "Operator methods in fractal analysis, wavelets and dynamical systems," December 2-7, 2006, organized by O. Bratteli, P. Jorgensen, D. Kribs, G. Olafsson, and S. Silvestrov, and discussed the interrelationships and differences between the articles, and worked on two open problems posed in the Larson-Massopust article. We solved part of Problem 2, including a surprising positive solution to a conjecture that was raised, and we present our results in this article.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Affine Weyl groups; Tilings; Wavelet sets
ISSN (print) / ISBN 0167-8019
Journal Acta Applicandae Mathematicae
Quellenangaben Volume: 108, Issue: 3, Pages: 529-546
Reviewing status Peer reviewed
Institute(s) Institute of Biomathematics and Biometry (IBB)