# Lattice tiling and the Weyl—Heisenberg frames

@article{Han2001LatticeTA,
title={Lattice tiling and the Weyl—Heisenberg frames
},
author={Deguang Han and Y. Wang},
journal={Geometric & Functional Analysis GAFA},
year={2001},
volume={11},
pages={742-758}
}
• Published 2001
• Mathematics
• Geometric & Functional Analysis GAFA
• Abstract. Let {\cal L} and {\cal K} be two full rank lattices in ${\Bbb R}^d$. We prove that if ${\rm v}({\cal L} ) = {\rm v}({\cal K})$, i.e. they have the same volume, then there exists a measurable set $\Omega$ such that it tiles ${\Bbb R}^d$ by both ${\cal L}$ and ${\cal K}$. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if ${\rm v}({\cal L}) \le {\rm v}({\cal K})$ then there exists a measurable set… CONTINUE READING
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