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arXiv · 1810.10870

Approximate Lattices and Meyer Sets in Nilpotent Lie Groups

Simon Machado
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Abstract

We show that uniform approximate lattices in nilpotent Lie groups are subsets of model sets. This extends a theorem due to Yves Meyer about quasicrystals in Euclidean spaces. To do so we study relatively dense subsets of simply connected nilpotent Lie groups and their logarithms. We then deduce a simple criterion for the existence of an approximate lattice in a given nilpotent Lie group.

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Simon Machado. 2018-10-25. Approximate Lattices and Meyer Sets in Nilpotent Lie Groups. https://doi.org/10.19086/da.11886

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