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Three-way tiling sets in two dimension | | David Larson
; Peter Massopust
; Gestur Olafsson
; | | Date: |
18 Oct 2007 | | Abstract: | In this article we show that there exist measurable sets W in the plane with
finite measure that tile the plane in a measurable way under the action of a
expansive matrix A, an affine Weyl group W, and a full rank lattice G. 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. | | Source: | arXiv, 0710.3520 | | Services: | Forum | Review | PDF | Favorites | |
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