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}
}
  • Deguang Han, Y. Wang
  • 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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