Abstract
LetL andK be two full rank lattices inR d . We prove that if v(L )=v (K), i.e. they have the same volume, then there exists a measurable set such that it tilesR d by both L andK. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) v(K) then there exists a measurable set such that it tiles byL and packs byK. Using these tiling results we answer a well known question on the density property of Weyl-Heisenberg frames.
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